A certain 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 6thplace, 7thplace, 8thplace, 9thplace, and 10thplace winner are each named. If 22 people enter this year, how many complete award announcements are possible?

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, .

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,

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

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

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

(3x-8) or (3x+8)

step-by-step explanation: