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Q.

A nine digit number is formed from 1,2,3,4,5 such that product of all digits is always 1920. The total number of ways is  393(9Pr) , where the value of ‘r’ is ______

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a

3

b

4

c

5

d

2

answer is D.

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Detailed Solution

1920=5×3×27=5×3×2×2×2×2×2×2×2=9!7!=9×8 1920=5×3×4×2×2×2×2×2=9!7!=9×8×7×6 1920=3,5,4,4,2,2,2,1,1 =9!2!2!3! 1920= 3,5,4,4,4,2,1,1,1  9!3!3! Total =  9!5!+9!2!2!3!+9!3!3!=9!7!(1+42+210+140) = 3939P2 

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