Q.1
How many words of 4 consonants and 3 vowels can be made from 12 consonants and 4 vowels, if all the letters are different?
Q.2
In a certain laboratory, chemicals are identified by a colour-coding system. There are 20 different chemicals. Each one is coded with either a single colour or a unique two-colour pair. If the order of colours in the pairs does not matter, what is the minimum number of different colours needed to code all 20 chemicals with either a single colour or a unique pair of colours?
Q.3
Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
Q.4
In how many ways can the letters of the word ‘MOMENT’ be arranged?
Q.5
There are 2 brothers among a group of 20 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two brothers?
Q.6
In how many different ways can the letters of the word ENGINEERING be arranged?
Q.7
In how many different ways can the letters of the word CORPORATION be arranged so that the vowels may occupy only the odd positions?
Q.8
In how many different ways can the letters of the word SOFTWARE be arranged in such a way that the vowels always come together?
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 at least 1 man?
Q.10
In how many ways can the letters of the word MATHEMATICS be arranged so that all the vowels always come together?
Q.11
A select group of 4 is to be formed from 8 men and 6 women in such a way that the group must have at least 1 women. In how many different ways can it be done ?
Q.12
In how many different ways can the letters of the word AUCTION be arranged in such a way that the vowels always come together?
Q.13
In how many different ways can the letters of the word MACHINE be arranged so that the vowels may occupy only the odd positions?
Q.14
a, b, c, d and e are five natural numbers. Find the number of ordered sets (a, b, c, d, e) possible such that a + b + c + d + e = 64.
Q.15
In how many different ways can the letters of the word JUDGE be arranged in such a way that the vowels always come together?
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
In how many different ways can the letters of the word DISPLAY be arranged?
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