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  • A bag contains 6 black marbles, 4 white marbles, and 2 gray marbles. How many different outcomes are possible if all the white and gray marbles are grouped together?<div class='qna-op

A bag contains 6 black marbles, 4 white marbles, and 2 gray marbles. How many different outcomes are possible if all the white and gray marbles are grouped together?

Option: 1

19030400


Option: 2

49020400 


Option: 3

29030400 

 


Option: 4

39020400


Answers (1)

best_answer

To determine the number of different outcomes when all the white and gray marbles are grouped together, we can consider the white and gray marbles as a single entity. This means we have three groups: the grouped white and gray marbles, the black marbles, and the remaining marble.

Grouping the white and gray marbles together as a single entity.

Since we have 4 white marbles and 2 gray marbles, there are 1 + 1 = 2! ways to arrange them among themselves.

Arranging the black marbles: We have 6 black marbles, which can be arranged among themselves in 6!

So, the total number of ways the marbles are arranged is given by,

6 !+1 !+1 !=8 !

Thus, the total number of outcomes is,

6 ! \times 8 !=720 \times 40320\\ 6 ! \times 8 !=29030400

Therefore, there are 29030400 different outcomes possible when drawing marbles from the bag if all the white and gray marbles are grouped together.

 

Posted by

himanshu.meshram

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