00:01
Here it is given that a bookshelf contains 3 different mathematics textbooks, 3 different engineering textbooks and 8 different history textbooks.
00:19
Hence this can be arranged in so, first question this can be arranged in 14 factorial ways.
00:25
Hence number of ways equal to 14 factorial which is 87178291200.
00:33
So, this is the final answer.
00:36
The second question so, here we have to find the number of ways the condition here is.
00:43
So, each book is arranged by category.
00:49
So, which is equal to first one 3 different math textbooks can be done in 3 factorial ways and 3 different engineering textbooks can be done in 3 factorial ways and 8 different history textbooks can be done in 8 factorial ways and these can be shuffled each other.
01:06
Therefore, it is again 3 factorial ways.
01:08
Hence the final answer is 4320 multiplied by 6 multiplied by 6 multiplied by 6.
01:17
So, it is 8709120...