00:00So, in this question, we are asked how many four-letter words, with or without meaning.
00:05Which means we can arrange them in any order, if it have meaning or not have meaning.
00:11Containing two vowels can be extracted from the letters of this word like now.
00:15So, first of all, no letter is repeated in this word. So, it will be simple answer.
00:21And then, how many vowels we have in it.
00:25So, there are five vowels as we know, A, E, I, O, U.
00:29So, here there are vowels U and O are vowels in it.
00:34So, it does not matter whatever we select, these two will be always selected.
00:39So, how many positions are vacant?
00:42Two letters have been selected.
00:45Remaining are five letters.
00:47From the remaining five letters, we have to select two more letters.
00:51Because we need to make a four-letter word.
00:54So, 5C2 formula we will put.
00:57Then, 5C2 is 5 into 4 divided by 2.
01:012 cancel by 2.
01:03This becomes 10.
01:04So, total vowels in 10 ways, we can select four letters.
01:10Now, we have selected letters in 10 ways.
01:14Now, how many possible orders can be arranged?
01:17Four letters.
01:18They are selected four letters.
01:21So, they can be arranged in formula direct.
01:244 factorial.
01:264 into 3 into 2 into 1.
01:30So, 4 into 3 is 12.
01:3212 into 2 is 24.
01:34This is direct formula of arrangement in case of no repetition.
01:39If repetition was allowed, then this will be 4 into 4 into 4 into 4.
01:44Why?
01:46Because first we will place one letter on it.
01:49Now, there are three options for the second place.
01:52Two options for the third place.
01:54Like this way.
01:56So, it will become 4 into 3 into 2.
01:5824.
01:59So, 24 into 10 is equal to 240.
02:03So, total 244 letter word can be made with content 2 vowels.
