How many eight digit no can be formed using $1, 1, 2, 2, 3, 3, 4, 5$ if no $2$ consecutive digits are identical.

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Theodore Discussed

How many eight digit no can be formed using

1, 1, 2, 2, 3, 3, 4, 5

if no

2

consecutive digits are identical.

10 mins ago

Discuss this question LIVE

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Text solutionVerified

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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Question Text	How many eight digit no can be formed using $1, 1, 2, 2, 3, 3, 4, 5$ if no $2$ consecutive digits are identical.
Answer Type	Text solution:1
Upvotes	150

How many eight digit no can be formed using 1,1,2,2,3,3,4,5 if no 2 consecutive digits are identical.

Text solutionVerified

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How many eight digit no can be formed using $1, 1, 2, 2, 3, 3, 4, 5$ if no $2$ consecutive digits are identical.