In an examination paper, there are two groups each containing 4 questions. A candidate is required to attempt 5 questions but not more than 3 questions from any group. In how many ways can 5 question be selected?
Answer: B 5 questions can be selected in the following ways:- 2 question from first group and 3 question from second group Or 3 question from first group and 2 question from second group. => (4C2*4C3) + (4C2*4C2) = 24 + 24 = 48.
Q. No. 14:
A box contains 10 balls out of which 3 are red and rest are blue. In how many ways can a random sample of 6 balls be drawn from the bag so that at the most 2 red balls are included in the sample and no sample has all the 6 balls of the same colour?
Answer: B Six balls can be selected in the following ways:- One red ball and 5 blue ball Or Two red balls and 4 blue balls Total number of ways = (3C1*7C5) + (3C2*7C4) = 63+105 = 168
Q. No. 15:
A class photograph has to be taken. The front row consist of 6 girls who are sitting. 20 boys are standing behind. The two corner positions are reserved for the 2 tallest boys. In how many ways can the students be arranged?
Answer: B Two tallest boys can be arranged in 2! ways, rest 18 can be arranged in 18! ways. Girls can be arranged in 6! ways. Total number of ways in which all the students can be arranged = 2! * 18! * 6! => 18! *1440
Q. No. 16:
In how many ways can a selection of 5 letters be made out of 5 A's, 4B's, 3C's, 2D's and 1E's?
Answer: D 5 letters out of 15 letters can be selected in 15P5 ways.
Q. No. 17:
Two series of a question booklet for an aptitude test are to be given to twelve students. In how many ways can the students be placed in two rows of six each so that there should be no identical series side by side and that the students sitting one behind the other should have the same series?
The number of ways in which a committee of 3 ladies and 4 gentleman can be appointed from a meeting consisting of 8 ladies and 7 gentleman, if Mrs X refuses to serve in a committee, if Mr. Y is its member, is