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The number of ways six distinct balls be distributed into 3 distinct urns. If each urn contain at least one ball are ____
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+3
It is equal to the no. of ONTO function from a set containing 6 elements to the set containing 3 elements.

= $3^6$  - ( 3C1 * $2^6$  - 3C2 * $1^6$ )

= $3^6$ - (189) = 729 - 189 = 540.
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Can you please explain in much more detail @Hemant
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Hemant Parihar please explain  - ( 3C1 * 2- 3C2 * 1)

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Yes exactly I am unable to understand this part

(3C1 * 26  - 3C2 * 1

+1

Read this it is from Rosen.

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check the last comment i tried distinct objects and distinct bins problem with restrictions
https://gateoverflow.in/191081/arrangement
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36 -(3C2 * 26  - 3C1 * 1)  :-

(3C2 * 26  - 3C1 * 1):- here we are removing the case when balls are distributed only between two persone(3C2 * 26 )  ...means balls are distributed either AB,BC or CA now for all these cases ...there is a chance that balls are given two only one (for AB only A or ONLY B) ...for all A,B,C this would happen two times there for we would add this one more time.....(3C1 * 16)

+1 vote
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