Question

# How many 7 digit numbers can be formed using the digits 1, 2, 0, 2, 4, 2, 4?

A
120
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B
360
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C
240
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D
424
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Solution

## The correct option is B 360There are 7 digits 1,2,0,2,4,2,4 in which 2 occurs 3 times, 4 occurs 2 times. ∴ Number of 7 digits numbers =7!3!×2!=420 But out of these 420 numbers, there are some numbers which being with '0' and they are not 7 digit numbers. The number of such numbers beginning with '0'. =6!3!×2!=60 Hence the required number of 7 digits numbers =420 - 60 = 360 Alternatively: 6654321⇒6.(6!) Since the leftmost place can assume only non-zero digit hence it can consider only 6 digits. Noe the remaining 6 places can be filled up in normal ways. But since 2 occurs 3 times, 4 occurs 2 times, therefore required number of 7 digit numbers =6.(6!)3!.2!=360

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