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  4. Consider the 10 lettered word W = C U R R I C U L U M. Number of ways in which 5 lettered words can be formed using the letters from the word 'W' if each 5 lettered word has exactly 3 different letters, is

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Q. Consider the 10 lettered word W = C U R R I C U L U M.
Number of ways in which 5 lettered words can be formed using the letters from the word 'W' if each 5 lettered word has exactly 3 different letters, is

Permutations and Combinations

Solution:

U's $\rightarrow 3 ; $ C's $\rightarrow 2 ;$ R's $\rightarrow 2 ;$ L's $\rightarrow 1 ;$ I's $\rightarrow 1 ;$ M's $\rightarrow 1$
Case-I : 3 Alike and 2 different
Number of words formed $=1 \times{ }^5 C _2 \times \frac{5 !}{3 !}=10 \times 20=200$.
Case-II: 2 Alike, 2 others alike and 1 different
Number of words formed $={ }^3 C _2 \times{ }^4 C _1 \times \frac{5 !}{2 ! 2 !}=12 \times 30=360$.