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Question

The total number of 6 digit numbers that can be made using digits 1,2,3,4, if all the digits should appear in the number at least once is

A
1560
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B
840
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C
1080
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D
480
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Solution

The correct option is A 1560
There can be two types of numbers.
(i) Any one of the digits 1,2,3,4 appears thrice and the remaining digits only once. i.e., of the type 1,2,3,4,4,4 etc.

Number of ways of selection of digit which appears thrice is 4C1.
Then the number of numbers of this type is (6!3!)×4C1=480

(ii) Any two of the digits 1,2,3,4 appears twice and the remaining two only once, i.e., of the type 1,2,3,3,4,4 etc.

The number of ways of selection of two digits which appear twice is 4C2.

Then the number of numbers of this type is 6!2!2!×4C2=1080

Therefore, the required number of numbers is 480+1080=1560.

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