Respuesta :
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 k items from n distinct items when the order of selection does not matters.
Whereas permutation is the number of ways to select k item from n 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, [tex]{22\choose 5}=\frac{22!}{5!(22-5)!} =26334[/tex].
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,
[tex]^{17}P_{5}=\frac{17!}{(17-5)!} =742560[/tex]
The total number of ways to select 10 winners of 22 is:
Total number of ways = 26334 × 742560 = 19,554,575,040.
