00:01
In this question, we're given the word arrangements.
00:04
So think note that the letter a, there's two of them.
00:08
Letter r, there's two.
00:10
Letter n, there's two.
00:12
Letter g, there's one.
00:14
Letter e, there's two.
00:16
Letter m, there's one.
00:18
Letter t, there's one.
00:19
And letter s, there's one.
00:21
Total number of letters are 12.
00:24
Now, in part a, you want to find the number of possible distinct arrangements of letters.
00:28
Now if i have n objects with r1, r2 all the way to rk repeats, the number of ways to permutate the n object with all these repeats will be n factorial over r1 factorial times r2 factorial all the way to rk factorial.
00:54
So in this case we have 12 letters.
00:59
So it's 12 factorial divided by two repeats for a.
01:04
There will be 2 factorial, 2 repeats for r will be 2 factorial, 2 repeats for n, there'll be 2 factorial, and 2 repeats for e, that will be 2 factorial.
01:15
So the number of ways will be this.
01:24
B want to find the number of possible distinct arrangements of the letters if, it starts with vowel, and the letter gs appear consecutively.
01:34
Now it's gs, not sg, so there's only one particular arrangement that's gs.
01:38
So i'm going to draw 12 slots to represent the alphabets 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12.
01:51
Now, the start must be a vowel.
01:53
So the vowels are a and e.
01:57
So it's either a or e in the first slot.
02:02
Now, gs can be in any slot...