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Total Probability Theorem

Question):- 7...

Question

Question):- 7 different balls are to be placed in three different boxes A, B, C. Find the probability that the first box will contain exactly three balls.

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Solution

Dear Student,

$T o t a l s a m p l e s i z e = N u m b e r o f w a y s o f p u t t i n g 7 b a l l s i n 3 b o x e s a n y b a l l c a n g o i n a n y o f t h e 3 b o x e s, s o e a c h b a l l h a s 3 c h o i c e s T o t a l n u m b e r o f w a y s = 3^{7} N o w t h e f a v o u r a b l e c a s e s w h e n f i r s t b o x c o n t a i n s e x a c t l y 3 b a l l s s o f i r s t s e l e c t 3 b a l l s o u t o f 7 b a l l s i n {}^{7}C_{3} w a y s T h a n o t h e r 4 b a l l s c a n g o i n a n y o f t w o b o x e s i n 2^{4} w a y s P r o b a b i l i t y = \frac{{}^{7}C_{3} \times 2^{4}}{3^{7}} = \frac{\frac{7 \times 6 \times 5}{6} \times 16}{3^{7}} = \frac{35 \times 16}{3^{7}}$
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