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In how many ways 5 different balls can be distributed into 3 boxes so that no box remains empty? |
Answer» The required number of ways `=3^(5)-.^(3)C_(1)(3-1)^(5)+.^(3)C_(2)(3-2)^(5)-.^(3)C_(3)(3-3)^(5)` `=243-96+3-0=150` Or Coefficient of `x^(5)` inn `5!(e^(x)-1)^(3)` =Coefficient of `x^(5)` in `5!(e^(3x)-3e^(2x)+3e^(x)-1)` `=5!((3^(5))/(5!)-3xx(2^(5))/(5!)+3xx(1)/(5!))=3^(5)-3*2^(5)+3=243-96+3=150` |
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