The number of permutations or the letters of the word EXAMINATION taken 4 at a time is

136

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2454

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2266

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None of these

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Solution

The correct option is B $2454$
The letters are:
E X A M I N T O
A I N
Thus, number of permutations taken $4$ at a time is the coefficient of $x^{4}$ in:
$4! \times {(1 + \frac{x}{1!} + \frac{x^{2}}{2!})}^{3} . {(1 + \frac{x}{1!})}^{5} => 3 \times {(2 + 2 x + x^{2})}^{2} . (2 + 2 x + x^{2}) . {(1 + x)}^{5} => 3 \times (4 + 8 x^{2} + x^{4} + 8 x + 4 x^{3}) . (1 + 5 x + 10 x^{2} + {10 x}^{3} + 5 x^{4} + x^{5}) . (2 + 2 x + x^{2}) => 3 \times {(20 + 80 + 1 + 80 + 20) .2 + (40 + 40 + 80 + 4) .2 + (40 + 8 + 40 + 20)} = 3 \times {402 + 328 + 108} = 3 \times 838 = 2514$
Hence, (b) is correct.

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Similar questions

Find the number of combinations and permutations of $4$ letters taken from the word 'EXAMINATION'.

4

E X A M I N A T I O N

H O N O L U L U

4

4

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