Q. 1 There are 5 boys and 4 girls in a class. A committee of 5 is to be selected such that there are 3 boys and 2 girls in the committee. In how many ways the committee can the committee be selected?. Also in how many ways can the committee be selected if there are at least one boy in the committee.
A) 40 ways
B) 50 ways
C) 60 ways
D) 70 ways
Ans. D
5C3 * 4C2
=10*6
=60 ways
Q.2 Distribute 50 kids into the groups of size 5,10,15 & 20 ?
A) 50! /( 5!*10!*20!15!)
B) 50! * 2! /( 5!*10!*20!15!)
C) 49!/2!( 5!*10!*20!15!)
D) None of the above
Ans. A
50C5 * 45C10 * 35C15 * 20C20
(50 of size 5) (Remaining 45 from 10) (Remaining 35 from 15)
Or 50! / (45!5!) * 45! (35!10!) * 35! (20! 15!) * 1
Or 50! / 5!*10! * 20! * 15!
Q.3 A person has eighth letters & eigth addressed envelopes corresponding to those letters. In how many ways can he put the letters in the envelopes such that exactly 5 of them get delivered correctly ?
A) 112ways
B) 113ways
C) 114ways
D) 115ways
Ans. A
Since five got delivered correct=8C5 ways
Therefore, 3 get delivered incorrectly i.e. dearrangement (3) = 2 ways
i.e. total ways = 2 * 8C5 = 2 * 56 = 112ways
Q.4 In how many ways can you distribute 7 identical chocolates in 5 kids :
I) When there is no restriction ?
A) 11C4
B) 10C4
C) 11C3
D) 10C3
Ans. A
Formula used:
(N+r-1)! / C(r-1) (where, n= no. of chocolates & r=kids)
Therefore, 11! / 7! 4!
= 11C4
II) in such a way each kid should get atleast one chocolate ?
A) 6C4
B) 6C3
C) 6C5
D) 6C2
Ans. A
Formula used:
(n-1) / C (r-1)
i.e. 6C4
Q.5 In how many ways can you distribute 5 distinct rings :
I) in four boxes;
A) 1024 ways
B) 1025 ways
C) 256 ways
D) 4096 ways
Ans. A
4 * 4 * 4 * 4 * 4 = 1024 ways
(1st ring in 4 boxes) (2nd ring in 4boxes) as on…
II) in 4 fingers
A) 8C3
B) 8C2
C) 8C4
D) 8C5
Ans. A
Formula used:
(N+r-1) / C(r-1)
Or (5+4-1) / C(4-1)
Or 8C3
