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प्रश्न
Find the number of distinct numbers formed using the digits 3, 4, 5, 6, 7, 8, 9, so that odd positions are occupied by odd digits
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उत्तर
Digits are 3, 4, 5, 6, 7, 8, 9
Odd places are 1st, 3rd, 5th and 7th and odd digits are 3, 5, 7, 9. Even places are 2nd, 4th and 6th and even digits are 2, 4, 6.
The four odd digits occupy 4 odd places in 4P4 ways and three even digits can occupy the remaining 3 even places in 3P3 ways.
∴ the total number of distinct numbers that can be formed
= 4P4 × 3P3 = 4!3!
= 4 × 3 × 2 × 1 × 3 × 2 × 1
= 144.
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