Four cash prizes ($5000, $2000, $500 and $250) to be awarded to 4 students selected randomly from 15 students ( 7 from ucf and 8 from uf). in how many ways the prizes can awarded?

32760 ways

Step-by-step explanation:

There are overall 15 students from which we have to select 4 students at random for the 4 Cash prizes.

i)                 First Prize can be distributed in ways .

Also here we know the identity which says that

Hence

Now we are left with 14 students for second prize.

ii)                   Second prize can be distributed in   ways

Now we are left with 13 students for third prize.

iii)                 Third prize can be distributed in   ways.

Now we are left with only one prize and which can be distributed among 12 Students

iv)                 Fourth prize can be distributed in   ways.

Hence total number of ways of distributing 4 prizes among 15 students is

= 32760