ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Fundamental Principle of Counting : Multiplication Principle

Updated on November 16, 2011

Fundamental Principle of Counting : Multiplication Principle

If an operation can be performed in any of n1 ways and if for each of these, a second operation can be performed in any of n2 ways , and if the first two operations have been performed, a third operation can be performed in any of n3 ways , and so on , then all these operations can be performed simultaneously in n1 * n2 * n3 ways.

Example One : Find the number of codes from the digits 4, 7, 8 (without repetition ).

Solution : 3 * 2 * 1 = 6 codes

That is the hundreds position can be chosen in three ways, the tens position in two ways and the units position in one way.

Example Two : Find the number of ways a voter can be classified if there are four income categories and five education categories,

Solution : 4 * 5 = 20 ways

Example Three: A furniture store has five warehouses and twelve retail outlets. In how many different ways can they ship an item from one of the warehouses to one of the stores?

Solution : 5 * 12 = 60 ways

Example Four : In how many ways can be a class of 35 students elect a president and a secretary assuming that no member can hold more than one position ?

Solution : 35 * 34 = 1, 190 ways

Example Five : In a doctor’s office, there are ten issues of Time magazine, six issues of Reader’s Digest and four issues of Asiaweeek . In how many ways can a patient waiting to see the doctor, glance at one of each type of magazine, if the order does not matter ?

Solution ; 10 * 6 * 4 = 240 ways

Example Six : How many number combinations are possible using three digits from 1 to 7 if repetition is allowed?

Solution : 7 * 7 * 7 = 343 ways.

Example Seven : In how many ways a 10-item True or False quiz be answered ?

Solution : 2^10 or 1024 ways







    0 of 8192 characters used
    Post Comment
    • cristina327 profile imageAUTHOR

      Cristine Abigail Santander 

      7 years ago from Manila

      Hi carcro great to see you on this Math hub. Thank you for taking time to visit this hub. Your visit and comments are much appreciated. Remain blessed and best regards.

    • carcro profile image

      Paul Cronin 

      7 years ago from Winnipeg

      I have always loved math. I guess I must be a nerd but its always come easy to me. Thanks for sharing your math tips with the masses!


    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at:

    Show Details
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the or domains, for performance and efficiency reasons. (Privacy Policy)
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)