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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?

Number of ways of finding a flag for place 1 = 5

rightwards double arrow

m = 5

Number of remaining flags = 4

Number of ways of finding a flag for place 2 to complete the signal = 4

rightwards double arrow

n = 4

∴ By fundamental principle of counting, the number of signals generated

=

straight m cross times straight n equals 5 cross times 4 equals 20

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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?

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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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9. How many 3 digit numbers are there without repetition?

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10. 3 men board a bus in which there are 5 vacant seats. In how many ways can they occupy the seats?

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