Wes asked in Science & MathematicsMathematics · 3 weeks ago

# 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
3 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
3 weeks ago

Answer is 7! = 5040

• 3 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.

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.

• 3 weeks ago

7!

And that's not me being excited.

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