00:01
Problem we are given a word committee c o double m i double t e you have to find the number of ways in which we can get the word such that four vowels do not come together for that first we'll find out the total number of ways in which the word committee can be arranged and then we'll subtract the ways in which the four wobbles always come together to get the number of words in which they never come together.
00:36
So let us first find the ways in which the word committee can be arranged.
00:41
Had it be, it has nine letters.
00:44
So if all these nine letters were different, the number of ways and it can be arranged is nine factorial.
00:51
Since m occurs twice, t occurs twice, and e occurred twice.
00:57
So we'll divide it by two factorial each to count for the internal arrangement of mte.
01:06
So 2m, 2t and 2.
01:10
Solving this, we get the value as 45360.
01:17
Now let's find the number of ways in which four wobbles always come together.
01:31
Mind that this is the total ways in which the word committee can be arranged.
01:40
So four vowels always come together.
01:41
The four vowels are o, i, e, e.
01:44
So this is one entity.
01:46
The other entities are c, double m and double t.
01:54
So we have one entity as oiwe, which is one set of four vowels that always come together...