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If a, b, c are three natural numbers in...

If `a, b, c` are three natural numbers in AP such that `a + b + c=21` and if possible number of ordered triplet `(a, b, c)` is `lambda`, then the value of `(lambda -5)` is

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The correct Answer is:
8
`a+b+c=21implies3b=21impliesb=7" "[because a+c=2b]`
`impliesa+b+c=21impliesa+c=14`
`implieslamda=.^(14-1)C_(2-1)=.^(13)C_(1)=13`
hence, `lamda-5=13-5=8`
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