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deff fn [24]
3 years ago
8

A certain mathematics contest has a peculiar way of giving prizes. Five people are named as Grand Prize winners, but their finis

hing order is not listed. Then from among the other entrants, a 6thplace, 7thplace, 8thplace, 9thplace, and 10thplace winner are each named.If 22 people enter this year, how many complete award announcements are possible?
Mathematics
1 answer:
bixtya [17]3 years ago
6 0

Answer:

The number of complete award announcements possible are 19,554,575,040.

Step-by-step explanation:

Combination is the number of ways to select <em>k</em> items from <em>n</em> distinct items when the order of selection does not matters.

Whereas permutation is the number of ways to select <em>k</em> item from <em>n</em> items when order of selection matters.

The number of people entering this year is 22.

The number of ways to select 5 people for Grand Prize is, {22\choose 5}=\frac{22!}{5!(22-5)!} =26334.

The remaining number of people is, 22 - 5 = 17.

It is provided that the other 5 are selected according to an order.

The number of ways to select other 5 winners is,

^{17}P_{5}=\frac{17!}{(17-5)!} =742560

The total number of ways to select 10 winners of 22 is:

Total number of ways = 26334 × 742560 = 19,554,575,040.

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