Question

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?

Answer 1

Answer:

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 $^{15}\textrm{C}_{1}$ ways .

Also here we know the identity which says that

$^{m}\textrm{C}_{1}=m$

Hence $^{15}\textrm{C}_{1}=15$

Now we are left with 14 students for second prize.

ii)                   Second prize can be distributed in $^{14}\textrm{C}_{1}=14$  ways

Now we are left with 13 students for third prize.

iii)                 Third prize can be distributed in $^{13}\textrm{C}_{1}=13$  ways.

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

iv)                 Fourth prize can be distributed in $^{12}\textrm{C}_{1}=12$  ways.

 

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

$15 \times 14\times 13\times 12$

= 32760