Q.1
Out of 5 men and 3 women, a committee of three members is to be formed so that it has 1 women, and 2 men. In how many different ways can it be done?
Q.2
In how many different ways can the letters of the word BANANA be arranged?
Q.3
In how many different ways can the letters of the word ‘TRANSPIRATION’ be arranged so that the vowels always come together?
Q.4
In how many different ways can the letters of the word CAPITAL be arranged so that the vowels always come together?
Q.5
Find the number of triangles which can be formed by joining the angular points of a polygon of 8 sides as vertices.
Q.6
A committee of 5 members is to be formed out of 3 trainees, 4 professors and 6 research associates. In how many different ways can this be done, if the committee should have 4 professors and 1 research associate or all 3 trainees and 2 professors?
Q.7
In how many different ways can the letters of the word OPERATE be arranged ?
Q.8
Out of 5 women and 4 men, a committee of three members is to be formed in such a way that at least one member is a women. In how many different ways can it be done ?
Q.9
A committee of 5 members is to be formed by selecting out of 4 men and 5 women. In how many different ways the committee can be formed if it should have 2 men and 3 women?
Q.10
In how many different ways can the letters of the word INCREASE be arranged?
Q.11
In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
Q.12
In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women ?
Q.13
How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
Q.14
In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?
Q.15
A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?
Q.16
In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
Q.17
How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
Q.18
In how many different ways can the letters of the word RUMOUR be arranged?
Q.19
In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?
Q.20
In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?
Q.21
In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
Q.22
In how many ways can the letters of the word MANAGEMENT be rearranged so that the two As do not appear together?
Q.23
How many numbers are there between 100 and 1000 such that at least one of their digits is 6?
Q.24
There are 6 equally spaced points A, B, C, D, E and F marked on a circle with radius R. How many convex pentagons of distinctly different areas can be drawn using these points as vertices?
Q.25
From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
Q.26
In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
Q.27
20 men handshake with each other without repetition. What is the total number of handshakes made?
Q.28
A student is required to answer 6 out of 10 questions divided into two groups each containing 5 questions. He is not permitted to attempt more than 4 from each group. In how many ways can he make the choice?
Q.29
While packing for a business trip Mr. Debashis has packed 3 pairs of shoes, 4 pants, 3 half-pants,6 shirts, 3 sweater and 2 jackets. The outfit is defined as consisting of a pair of shoes, a choice of "lower wear" (either a pant or a half-pant), a choice of "upper wear" (it could be a shirt or a sweater or both) and finally he may or may not choose to wear a jacket. How many different outfits are possible?
Q.30
In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
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