1.

In how many ways can letter of the word leopard be arranged if no two consonants are together

Answer»

Answer should be 4320

No of ways in which VOWELS are together = no of ways in which exactly two vowels are together + no of ways in which 3 vowels are together.

But if you just choose 2 vowels in 3C2 and consider it as a set , you will have this set, one remaining vowel and 4 other consonants.
If you rearrange these it ALSO covers set containgin 3 vowels together.
so you have 2 * 3C2 * 5! as invalid combinations

No of ways to arrange 7 LETTERS = 7! = 5040

Desired ways = 5040 - 2 * 3C2 * 5! = 4320


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