Question
Thu October 04, 2012 By: Koushtav Chakrabarty
1st Q:
I mean i there are 3 bowls and 7 toys. So why is th no. of ways 37 and not 3 times 7.
 
And I didnt understand the question properly.
 

Sir, I didn't understand that toy and bowl example ( IN HOW MANY WAYS CAN 7 TOYS BE DISTRIBUTED IN 3 BOWLS/IN HOW MANY WAYS CAN 7 TOYS BE DISTRIBUTED IN 3 BOWLS SUCH THAT EACH BOWL HAS AT LEAST ONE TOY)in the video.

Expert Reply
Thu November 08, 2012
1) 

As we know there are three choices (3 bowls) for each of the 7 toys.  Therefore, by  the fundamental principle of multiplication ,the

total number of ways = 3 x 3 x 3 x 3 x 3 x 3 x 3 = 37= 2,187 ways.

2)

Any three toys can be arranged in 3 bowls in 3! = 6 ways,
Now remaining 4 toys where a bowl can hold any number of toys.
So number of ways of putting those 4 toys in 3 bowls is 34 = 81.
Total number of ways = 6x81 = 486
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