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Q.
Total number of distinct 4 letters words that can be formed from the letters of the word 'NANDINI'. so that at most 2 alike letters are together, is -
Permutations and Combinations
Solution:
$3$ alike and $1$ distinct $\rightarrow{ }^{1} C _{1} \times{ }^{3} C _{1} \times\left[\frac{4 !}{3 !}-2 !\right]=6$
$2$ alike $2$ distinct $\rightarrow{ }^{2} C _{2} \times\left(\frac{4 !}{2 ! 2 !}\right)=6$
$2$ alike and $2$ distinct $\rightarrow{ }^{2} C _{1} \times{ }^{3} C _{2} \times \frac{4 !}{2 !}=72$
4 distinct $\rightarrow 4 !$