Jennifer has 10 boxes with her.In how many ways can she arrange them so that 4 of the boxes do not remain together.?
Answers
Given : Jennifer has 10 boxes with her. She arrange them so that 4 of the boxes do not remain together
To find : Number of ways she can arrange
Solution :
10 boxes can be arranged in 10! ways
4 of the boxes do not remain together
= Total ways - 4 of the boxes remain together
10 boxes = 6 Boxes + 4 Boxes
4 of the boxes remain together
take 4 boxes as 1 box which can be arranged in 4! ways
Total boxes = 6 + 1 = 7 boxes
7 Boxes can be arranged in 7! Ways
Total ways of arranging 4 of the boxes remain together
7!.4!
4 of the boxes do not remain together = Total ways - 4 of the boxes remain together
= 10! -7!.4!
= 7! ( 10 * 9 * 8 - 24)
= 7! ( 696)
= 35,07,840
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Given:
- Jennifer has 10 boxes
________________________________
To Find:
- Number of ways to arrange those boxes so that 4 of the boxes do not remain together.
________________________________
Solution:
The number of ways the 10 boxes can be arranged.➛
10! ways.
✏️If we subtract the possibility of the 4 boxes remaining together
such as:-
4 boxes = 1 unit ,
Remaining 6 boxes = 6 units .
Total = 7 units
7 units can be arranged in 7! ways
and the 4 boxes can be arranged among themselves in 4! ways.
Therefore, the answer is 10!-(7!*4!).
_____________________________
Answer:
10!-(7!*4!)