A. 9

**B. 12**

C. 14

D. 18

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# Permutations and Combinations

## A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?

A. ¹²C₅ * 10

B. ¹²C₇ * 10

**C. ¹²C₇ * ¹⁰C₅**

D. 12 * ¹⁰C₅

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## In how many ways can live boys and three girls sit in a row such that all boys sit together?

A. 4800

B. 5760

**C. 2880**

D. 15000

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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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## 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

## A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons?

**A. 165**

B. 185

C. 205

D. 225

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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

## How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}

**A. 60**

B. 360

C. 120

D. 240

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## The number of permutations of the letters of the word ‘MESMERISE’ is___________?

**A. 9!/(2!) ^{2} 3!**

B. 9!/(2!)

^{3}3!

C. 9!/(2!)

^{2}(3!)

^{2}

D. 5!/(2!)

^{2}3!

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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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