These are three pots and four coins. All these coins are to be distrib

1.	These are three pots and four coins. All these coins are to be distributed into these pots where any pot can contain any number of coins. Column1Column2(A)The number of ways in which all these coins can be(P)3distributed if all coins are identical but all pots are different(B)The number of ways in which all these coins can be(Q)6distributed if all coins are different but all pots are identical(C)The number of ways all these coins can be distributed such(R)15that no pot is empty if all coins are different but all pots areidentical.(D)The number of ways all these coins can be distributed(S)14such that no pot is empty is all coins are identical but all pots are different.
Answer» These are three pots and four coins. All these coins are to be distributed into these pots where any pot can contain any number of coins. $\begin{matrix} C o l u m n 1 & C o l u m n 2 (A) & T h e n u m b e r o f w a y s i n w h i c h a l l t h e s e c o i n s c a n b e & (P) & 3 d i s t r i b u t e d i f a l l c o i n s a r e i d e n t i c a l b u t a l l p o t s a r e d i f f e r e n t (B) & T h e n u m b e r o f w a y s i n w h i c h a l l t h e s e c o i n s c a n b e & (Q) & 6 d i s t r i b u t e d i f a l l c o i n s a r e d i f f e r e n t b u t a l l p o t s a r e i d e n t i c a l (C) & T h e n u m b e r o f w a y s a l l t h e s e c o i n s c a n b e d i s t r i b u t e d s u c h & (R) & 15 t h a t n o p o t i s e m p t y i f a l l c o i n s a r e d i f f e r e n t b u t a l l p o t s a r e i d e n t i c a l . (D) & T h e n u m b e r o f w a y s a l l t h e s e c o i n s c a n b e d i s t r i b u t e d & (S) & 14 s u c h t h a t n o p o t i s e m p t y i s a l l c o i n s a r e i d e n t i c a l b u t a l l p o t s a r e d i f f e r e n t . \end{matrix}$

These are three pots and four coins. All these coins are to be distributed into these pots where any pot can contain any number of coins. Column1Column2(A)The number of ways in which all these coins can be(P)3distributed if all coins are identical but all pots are different(B)The number of ways in which all these coins can be(Q)6distributed if all coins are different but all pots are identical(C)The number of ways all these coins can be distributed such(R)15that no pot is empty if all coins are different but all pots areidentical.(D)The number of ways all these coins can be distributed(S)14such that no pot is empty is all coins are identical but all pots are different.

Answer»

These are three pots and four coins. All these coins are to be distributed into these pots where any pot can contain any number of coins.

$\begin{matrix} C o l u m n 1 & C o l u m n 2 (A) & T h e n u m b e r o f w a y s i n w h i c h a l l t h e s e c o i n s c a n b e & (P) & 3 d i s t r i b u t e d i f a l l c o i n s a r e i d e n t i c a l b u t a l l p o t s a r e d i f f e r e n t (B) & T h e n u m b e r o f w a y s i n w h i c h a l l t h e s e c o i n s c a n b e & (Q) & 6 d i s t r i b u t e d i f a l l c o i n s a r e d i f f e r e n t b u t a l l p o t s a r e i d e n t i c a l (C) & T h e n u m b e r o f w a y s a l l t h e s e c o i n s c a n b e d i s t r i b u t e d s u c h & (R) & 15 t h a t n o p o t i s e m p t y i f a l l c o i n s a r e d i f f e r e n t b u t a l l p o t s a r e i d e n t i c a l . (D) & T h e n u m b e r o f w a y s a l l t h e s e c o i n s c a n b e d i s t r i b u t e d & (S) & 14 s u c h t h a t n o p o t i s e m p t y i s a l l c o i n s a r e i d e n t i c a l b u t a l l p o t s a r e d i f f e r e n t . \end{matrix}$

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