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Permutations and Combinations

Short Answer Type

1. Given 5 flags of different colours, how many different signals can be generated if each signal requires use of 2 flags, one below the other?

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Long Answer Type

A class has 30 students. In how many ways can three prizes be awarded so that:

(a) no students get more than one prize?

(b) a student may get any number of prizes?

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Short Answer Type

3. A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

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How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed.

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How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is not allowed.

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Long Answer Type

6. How many 3-digit odd numbers can be formed from the digits 1,2,3,4,5,6 if:

(a) the digits can be repeated (b) the digits cannot be repeated?

(a) Number of digits available = 6

Number of places [(x), (y) and (z)] for them = 3

Repetition is allowed and the 3-digit numbers formed are odd

Number of ways in which box (x) can be filled = 3 (by 1, 3 or 5 as the numbers formed are to be odd)

rightwards double arrow

m = 3
Number of ways of filling box (y) = 6 (∴ Repetition is allowed)

rightwards double arrow

n = 6

Number of ways of filling box (z) = 6 (∵ Repetition is allowed)

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p = 6

∴ Total number of 3-digit odd numbers formed

= m x n x p = 3 x 6 x 6 = 108

(b) Number of ways of filling box (x) = 3 (only odd numbers are to be in this box )

rightwards double arrow

m = 3

Number of ways of filling box (y) = 5 (∵ Repetition is not allowed)

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n = 5

Number of ways of filling box (z) = 4 (∵ Repetition is not allowed)

rightwards double arrow

p = 4

∴ Total number of 3-digit odd numbers formed

= m x n x p = 3 x 5 x 4 = 60.

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Short Answer Type

7. How many 5-digit telephone numbers can be constructed, using the digits 0 to 9 if each number starts with 67 and no digit appears more than once ?

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8. Find the number of different signals that can be generated by arranging at least 2 flags in order (one below the other) on a vertical staff, if five different flags are available.

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