Permutation and Combination

Question

Cricket team of 5 players can be selected from 5 girls and 6 boys such that selected team includes at least 2 boys.

a) 467

b) 461

c) 431

d) None

Solution

We have to select 5 players from 5 girls and 6 boys. There has to be 2 boys.

Case1: 2 boys and 3 girls !!= \ ^6C_2 xx \ ^5C_3= 150!!

Case2; 3 boys and 2 girls !!= \ ^6C_3 xx \ ^5C_2= 200!!

Case3: 4 boys and 2 girl !!= \ ^6C_4 xx \ ^5C_1= 75!!

Case4: 5 boys and no girl !!= \ ^6C_5 xx \ ^5C_0=6!!

Adding all the cases, we get no. of total ways to choosing

!!=> 150+200+75+6 = 431!!

Option (c) is correct.

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