Q.

The number of different seven digit numbers that can be written using only the three digits 1, 2 and 3 with the condition that the digit 2 occurs exactly twice in each number is

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a

7P2 . 25

b

7C2 . 25

c

7C2 . 52

d

7C2 . 10

answer is B.

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Detailed Solution

We have to select 2 places for the digit 2. This can be done in7c2  ways Remaining each place can be filled in 2 ways(1,3) =7c2.25
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The number of different seven digit numbers that can be written using only the three digits 1, 2 and 3 with the condition that the digit 2 occurs exactly twice in each number is