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The number of permutations of the letters of the word AGAlN ta

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The number of permutations of the letters of the word AGAlN taken three at a time is

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Text solutionVerified

Number of letters in the word A G A l N are

=

5 out of which 2A, 1G, 1N, 1I

∴

Number of permutations taken three at a time

=

Coefficient of

x^{3}

3! (1 + \frac{x}{1 !} + \frac{x ^{2}}{2 !}) (1 + x)^{3}

=

Coefficient of

x^{3}

(\frac{6 ( 2 + 2 x + x ^{2}}{2}) (1 + x)^{3}

=

Coefficient of

x^{3}

3 {1 + (1 + x)^{2}} (1 + x)^{3}

=

Coefficient of

x^{3}

3 {(1 + x)^{3} + (1 + x)^{5}}

= 3 {^{3} C_{3} +^{5} C_{3}} = 3 (1 + 10) = 33

Hence, (d) is correct answer.

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Question Text	The number of permutations of the letters of the word AGAlN taken three at a time is
Answer Type	Text solution:1
Upvotes	150