Mixed Problems


 
 
Concept Explanation
 

Mixed Problems On Permutation And Combinations

Let us consider some practical problem where both permutations and combination are used.

Illustration: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed ?

Solution Three consonants out of 7 and 2 vowels out of 4 can be chosen in

^7C_3times ^4C_2 ways.

Thus, there are ^7C_3times ^4C_2 groups each containing 3 consonants and 2 vowels.

Since each group contains 5 letters, which can be arranged among themselves in 5! ways.

Hence, the required number of words = (^7C_3times ^4C_2)times 5!=25200.

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