How many eight digit no can be formed using 1, 1, 2, 2, 3, 3, 4, 5 | Filo
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Class 11

Math

Algebra

Permutations and Combinations

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How many eight digit no can be formed using if no consecutive digits are identical.

Solution: Odd digits cannot occupy odd places,so odd digits should occupy even places i,e 4 possiblities and odd numbers are three.
1) So selecting three positions from 4 positions can be done in 4C3 ways that is 4 ways.
2) Filling the three positions with three numbers can be done is 3! ways but 1,1 are identical so total number of ways is 3!/2! i,e 3
Now filling the remaining 5 positions can be done in 5! ways but again 2,2,2 are identical and 4,4 are identical so number of ways is 5!/(3!*2!)
i,e in 10 ways  so the total number of ways is 
4*3*10=120.
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