Question

(a) How many different committees consisting of 3 males and 4 females can be chosen from a group of 8 males and 7 females?

(b) In how many ways can 5 essays be ranked in a contest?

(c) A license plate has three letters from 26 letters of an alphabet and four digits from 0,1,2,3,4,5,6,7,8,9. How many plates can be made if:

i) letters and numbers cannot be repeated?

ii) repetitions are allowed?

Answer 1

(a)

3 males can be chosen from 8 males in

4 females can be chosen from 7 females in

So,

Number of different committees= 56 X 35 = 1960

So,

Answer is:

1960

(b)

Number of ways = 5! = 5 X 4 X 3 X 2 X 1 = 120

So,

Answer is:

120

(c)

(i)

First letter can be chosen in 26 ways

Second letter can be chosen in 25 ways

Third letter can be chosen in 24 ways

First digit can be chosen in 10 ways

Second digit can be chosen in 9 ways

Third digit can be chosen in 8 ways

Fourth digit can be chosen in 7 ways

So,

Number of plates = 26 X 25 X 24 X 10 X 9 X 8 X 7 = 78,624,000

(ii)

First letter can be chosen in 26 ways

Second letter can be chosen in 26 ways

Third letter can be chosen in 26 ways

First digit can be chosen in 10 ways

Second digit can be chosen in 10 ways

Third digit can be chosen in 10 ways

Fourth digit can be chosen in 10 ways

So,

Number of plates = 26 X 26 X 26 X 10 X 10 X 10 X 10 = 175,760,000