1 If three identical prizes are available for a contest with

1. If three identical prizes are available for a contest with 20 entrants, in how many ways the prizes can be distributed??

a. C(20,3)

b. P(20,3)

c. C(3,20)

d. P(3,20)

2. 7 persons compete in a race, in how many ways can the 1st,2nd and 3rd awards be distributed, if only one person receives each award??

a. C(7,3)

b. P(7,3)

c. C(3,7)

d. P(3,7)

How to choose which one is permutation and which one is a combination. Please explain briefly. am struggling with all permutation and combination problems. Thanks in advance.

Solution

1.) three identical prizes are available for a contest with 20 entrants, in how many ways the prizes can be distributed??

nCr where n = sample space and r things are selected.

20C3

Here the prizes are all same and order doesnt matter so, we can apply combination as we have to select 3 out of 20

2)

nPr - permutation calculator finds the number of different permutations of n distinct objects taken r at a time

7P3

Here we have 3 prizes 1st , 2nd and 3rd where odere matters we apply permutation