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.

.there can be infinite values of m and n that can satisfy the above equation. for each value of m of m or n. there maybe infinite sets of solution for the above

step-by-step explanation:

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.