There are 5 distinct paintings and 7 picture nails. In how many ways can the 5 paintings be hung from the 7 picture nails.?

2019-11-16 5:38 am
If we think of the picture nails as slots
we have
___ ___ ___ ___ ___ ___ ___
1 2 3 4 5 6 7

There will be two blank slots.

回答 (1)

2019-11-16 7:30 am
7P5 = 7 * 6 * 5 * 4 * 3
= 2,520

If you still aren't sure how to get that answer, think of each painting.
There are 7 choices of where to hang the first painting.
There are 6 choices of where to hang the second painting.
There are 5 choices of where to hang the third painting.
There are 4 choices of where to hang the fourth painting.
There are 3 choices of where to hang the fifth painting.

So the total ways would be:
7 * 6 * 5 * 4 * 3
= 2,520 ways


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