Test has 7 definitions to be paired with 7 words. Assuming each word corresponds to 1 definition, how many different matches are possible?

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  • geezer
    Lv 7
    4 weeks ago

    This sounds like a trick question to me,

    because your question says ''matches'' and not ''choices''.

    7 words .. 7 definitions

    If each word only coresponds to one definition that's only 7 ''matches''

    because words don't ''match'' the wrong definition.

    Think about it ....

    Take the first definition.

    That doesn't give you 7 ''matches'' if only 1 is correct .. does it ?

    There is only 1 ''match'' each time.

  • nbsale
    Lv 6
    4 weeks ago

    Answer is 7! = 5040

  • 4 weeks ago

    For the first definition, you have 7 choices of word.

    For the second definition, you have 6 choices of word.

    For the third, 5 choices

    For the fourth, 4 choices

    etc.

    7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040 matches

    In general, if you have n items, there are n! (factorial) ways to arrange them. So in this case you have 7 items (words) to arrange.

    Answer:

    7! = 5040 matches

    P.S. There is only 1 match that is correct. So if the arrangement is chosen completely at random, the probability of being correct is 1/5040.

  • 4 weeks ago

    7!

    And that's not me being excited.

    Think about it. 7 possible pairings for the first word. 6 for the second...

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