Question

Find the number of distinct numbers formed using the digits 3,4,5,6,7,8,9, so that odd position are occupied by odd digits

Answer 1

Given:

Seven digits 3, 4, 5, 6, 7, 8, 9

To find:

Number of distinct numbers so that odd positions are occupied by the odd digits.

Solution:

Total digits to be used = 7

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Odd  Even  Odd  Even  Odd  Even Odd

Number of odd positions in a number having all 7 digits = 4

Number of even positions in the number with 7 digits = 3

Therefore, total numbers formed by using these odd digits = 4! = 24

And the numbers formed formed by arranging even digits = 3! = 6

Total numbers that can be formed so that the odd positions are occupied by odd digits = 24 × 6 = 144