00:01
In its question, we're given there are six different math books and five different english books, and four math and three english books are to be chosen from the books above.
00:13
The seven books are to be arranged on a shelf.
00:16
There is arranged in a row.
00:19
In general, if i have n distinct objects, arranged in a row, it would be n factorial ways.
00:37
So the number of ways to arrange the seven books, if there are no restriction.
00:41
So that would be from the six math book i'm going to choose four of them.
00:46
N.
00:48
N is times or is plus.
00:52
So n times.
00:54
From the five english books, i'm going to choose three of them.
01:00
And for the seven books to arrange in a row, it will be seven factorial ways.
01:07
And so that would be 756 .000, zero, zero ways.
01:15
B, you want to find the number of ways to arrange in a row.
01:17
The seven books if the math books remain together.
01:22
So i'm just going to draw a block here.
01:24
I'm going to put in the four math book and the other three english books can be spread around it.
01:31
So for the four math book, there is four factorial ways to arrange themselves among themselves in this block.
01:40
So the block is to keep the math book together.
01:43
And this block is treated as one entity.
01:47
And the english books here, each one is treated as separate individual entities...