Given four integers X, Y, M and N. The task is to find the number of ways to form a word by choosing X number of vowels and Y number of consonants from total numbers of M vowels and N consonants.
Input : X = 2, Y = 2, M = 3, N = 3
Output : 216
The total number of ways of choosing 2 vowels from a total number of 3 vowels is i.e 3
The total number of ways of choosing 2 consonants from a total number of 3 consonants is i.e 3.
The total number of ways of selecting 2 consonants from 3 and 2 vowels from 3 is * = 9
The total number of ways of arranging 4 letters among themselves = 4! = 24
Hence, the required number of ways = 24 * 9 = 216
Input : X = 1, Y = 2, M = 2, N = 3
Output : 36
- The total number of ways of choosing X vowels from a total number of M vowels is
- The total number of ways of choosing Y consonants from a total number of N consonants is
- The total number of ways of selecting Y consonants from N and X vowels from M is *
- The total number of ways of arranging (X+Y) letters among themselves = (X+Y)!
- Hence, the required number of ways = (X+Y)! * *
Below is the implementation of the above approach:
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