00:01
Hello everyone.
00:02
So in this question we are given that there are total seven consonants while five vowels.
00:09
Now we need to tell that how many works can be formed if we select four different consonants out of seven consonants and three different vowels out of the five given vowels.
00:20
So for that here we will be using the concept of permutation and combination.
00:26
So here as we have to select four consonants from the given seven consonants from the given seven so therefore we will be having 7 c 4 that means out of the 7 consonants 4 gets selected now this will be multiplied by here we have 5 hours while 3 gets selected so therefore it will be 5 c 3 now the total alphabet selected is 4 plus 3 which is 7 now these 7 alphabets will get arranged among themselves so therefore this will be multiplied by 7 factorial.
01:10
Now in order to simplify this we will be using the formula of ncr.
01:17
So the formula of ncr is equal to the value of n factorial divided by the value of r factorial multiplied by an.
01:31
N minus r whole factorial.
01:35
Now we can see that in order to solve this, here the value of n will be 7 and r will be 4.
01:44
So we will be having that this will be equal to 7 factorial divided by 4 factorial multiplied by.
01:56
So here it will be 7 minus 4 which is 3.
02:00
So here we will have 3 factorial.
02:03
Now this will be multiplied by 5c3.
02:07
Again using the same formula, here we will have with us 5 factorial divided by 3 factorial multiplied by.
02:16
So 5 minus 3 is 2.
02:18
So we get 2 factorial here.
02:20
And this whole is multiplied by 7 factorial...