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Permutations and Combinations

Permutations and Combinations

In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together?

A. 10080
B. 4989600
C. 120960
D. None of these

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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?

A. 40
B. 400
C. 5040
D. 2520

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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?

A. 63
B. 90
C. 126
D. 45

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In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position?

A. 9
B. 12
C. 14
D. 18

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There are two identical red, two identical black, and two identical white balls.In how many different ways can the balls be placed in the cells (Each cell to contain one ball) shown above such that balls of the same colour do not occupy any two consecutive cells?

A. 15
B. 18
C. 24
D. 30

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Twelve people from a club, by picking lots. One of them will host a dinner for all once in a month. The number of dinners a particular member has to host in one year is________?

A. One
B. Zero
C. Three
D. Cannot be determined

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A person ordered 5 pairs of black socks and some pairs of brown socks. The price of a black pair was thrice that of a brown pair while preparing the bill the bill clerk inter-changed the number of black and brown pairs by mistake which increased the bill by 100% what was the number of pair of brown socks in the original order?

A. 10
B. 15
C. 20
D. 25

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A two number committee comprising of one male and the female number is to be constituted out of five male and 3 females. Amongst the females, Ms. A refused to be number committee in which Mr.B is taken as the number of how many different ways can the committee be constituted?

A. 11
B. 30
C. 14
D. 20

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A selection is to be made for one post of principal and two posts of vice-principal amongst the six candidates called for the interview only two are eligible for the post of principal while they all are eligible for the post of vice-principal. The number of possible combinations of selectees is___________?

A. 4
B. 12
C. 18
D. None of these

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A student has to opt for 2 subjects out of 5 subjects for a course. Namely commerce, economics, statistics, mathematics 1 and Mathematics 2, Mathematics 2 can be offered only if mathematics 1 has also opted. The number of different combinations of two subjects which can be opted is_________?

A. 5
B. 6
C. 7
D. 18

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