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The number of 6 digit numbers that can be made with the digits 1,2,3 and 4 and having exactly two pairs of digits, is

The number of 6 digit numbers that can be made with the digits 1,2,3 and 4 and having exactly two pairs of digits, is

Grade:12

2 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
7 years ago
exactly two pairs means we can pair 1,2 with 3,4 and so on

Hence, 2 pairs = 4 numbers

hence all 4 numbers should be included

so number of 6 digit numbers which can be formed by using thedigits 1,2,3 and 4.

4^6

Lavya
15 Points
5 years ago
Choose the repeat digits from {1,2,3,4} in C(4,2) ways then the remaining two digits take care of themselves since we are not allowed any more pairs. 
Now we have 6 numbers with 2 pairs and 2 singles which may be permuted in 6!/(2!2!1!1!) ways: 

C(4,2)*6!/(2!2!1!1!) = 1080

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