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in Permutations by (50.8k points)
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Find the total number of arrangements of the letters in the expression a3 b2 c4 when written at full length.

1 Answer

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Best answer

Here's 9 (i.e powers 3 + 2 + 4 = 9) objects in the expression a3 b2 c4 and there are 3 a’s, 2 b’s, 4 c’s

Therefore by using the formula,

n!/ (p! × q! × r!)

The total number of arrangements = 9! / (3! 2! 4!)

= [9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1] / (3 × 2 × 1 × 2 × 1 × 4 × 3 × 2 × 1)

= 7 × 6 × 5 × 3 × 2 × 1

= 1260

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