1.
In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together.
Answer: Option 'A'
Answer: Option 'A'
2.
In how many different number of ways a Committee of 3 person of can be selected from 5 men and 3 women such that atleast 1 women is included in the committee.
Answer: Option 'B'
1W 2M 2W 1M 3W
= 3C1 × 5C2 + 3C2 × 5C1 + 3C3s
= 3 × (5 × 4)/2 + 3 × 5 + 1
= 30 + 15 + 1 = 46
Total 5M 3W
8C3 = 56
5C3 = 10
Atleast one women = total - with out women
Atleast one women = 56 - 10 = 46
3.
In how many different number of ways the letters of the word 'ENGINEERING' can be arranged.
Answer: Option 'C'
11!/(3! × 3! × 2! × 2! × 1!)
= (11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)/(3 × 2 × 3 × 2 × 2 × 2 × 1)
= 11 × 10 × 8 × 7 × 5 × 3
= 277200
4.
In how many different number of ways 4 boys and 2 girls can sit on a bench?
Answer: Option ''
Answer: Option 'C'
npn = n!
6p6
= 6 × 5 × 4 × 3 × 2 × 1 = 720
5.
Find 102C99?
Answer: Option 'B'
102C99
= 102!/(102-99)!99!
= 102!/(3! × 99!)
= (102 × 101 × 100)/(3 × 2)
34 × 101 × 50 = 171700.