1. Identify the given digits:
The number is 223355888.
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Even digits: 2, 2, 8, 8, 8 (Total = 5 digits)
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Odd digits: 3, 3, 5, 5 (Total = 4 digits)
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Total digits: 9
2. Identify the positions:
In a nine-digit number, the positions are:
1, 2, 3, 4, 5, 6, 7, 8, 9
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Even positions: 2nd, 4th, 6th, and 8th (Total = 4 positions)
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Odd positions: 1st, 3rd, 5th, 7th, and 9th (Total = 5 positions)
3. Arrange the Odd Digits:
The 4 odd digits (3, 3, 5, 5) must occupy the 4 even positions.
The number of ways to arrange these is:
4. Arrange the Even Digits:
The remaining 5 even digits (2, 2, 8, 8, 8) must occupy the 5 odd positions.
The number of ways to arrange these is:
Ways (Even)=2×6120=12120=10
5. Total Number of Ways:
Using the multiplication principle, multiply the ways for odd and even digits:
The correct option is (c) 60.
