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Find the number of n digit numbers, whic...

Find the number of `n` digit numbers, which contain the digits 2 and 7, but not the digits 0, 1, 8, 9.

Text Solution

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The correct Answer is:
`6^(n)-2xx5^(n)+4^(n)`
Number of n-digit number formed by using the digits 2,3,4,5,6,7 is `6^(n)`.
Number of n-digit numbers formed by using the digits 3,4,5,6,7 is `n(A)=5^(n)`.
Number of n-digit numbers formed by using the digits 2,3,4,5,6 is `n(B)=5^(n)`.
Number of n-digit numbers formed by using the digits 3,4,5,6 is `n(A cap B)=4^(n)`.
So, total number of numbers which contains digits 2 and 7 is `6^(n)-5^(n)-5^(n)+4^(n)`.
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