1
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Question

# How many five-digit numbers (repetition is not allowed) can be formed by using digits 1-7, if two is always there in the number?

A
1200
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B
1800
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C
2400
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D
5400
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Solution

## The correct option is B 1800As two is already included, four more digits are required to be selected out of 6 digits. The number of ways of selecting the numbers = 6C4 = 6C2 = 15 ways Also, five digits can be arranged amongst themselves in 5! = 120 ways. Hence the total no. of possibilities =120×15=1800 ways.

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