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Question

A 7-digit number is formed using the digits from 1,2,3,,9 such that exactly one digit is repeated thrice and exactly one digit is repeated twice. The total number of such 7-digit number is

A
9×9×9×8×8×7×6
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B
9C1× 8C1× 7C5×7!3!×2!
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C
9C2× 7C5×7!5!
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D
7!3!×2!
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Solution

The correct option is B 9C1× 8C1× 7C5×7!3!×2!

Number of ways of selecting one digit which is repeated thrice is 9C1
Number of ways of selecting one digit which is repeated twice is 8C1
Number of ways of selecting remaining digits is 7C2

Total possible numbers =9C1×8C1×7C2×7!3!×2!

(Divided by 3!×2! because one digit is repeated 3 times and one digit is repeated 2 times)


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