Acertain mathematics contest has a peculiar way of giving prizes. five people are named as grand prize winners, but their finishing order is not listed. then from among the other entrants, a 6th place, 7th place, 8th place, 9th place, and 10th place winner are each named. if 22 people enter this year, how many complete award announcements are possible?

19554575040

Explanation:

The first five positions to be named as Grand Prize winners are not give any order.

Therefore, the number of ways they can be selected is

Now the remaining 5 positions are selected from the remaining 17 entries. So they can be ordered as,

17 x 16 x 15 x 14 x 13 ways of ordering

Therefore, the number of ways in which the entries can be announced is

= 19554575040 number of ways

Thus the announcement can be made in 19554575040 number of ways.

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