Permutation and Combination

Question

An Entrepenuer wants to assign 5 different jobs to 3 of his employees. If every employee is assigned atleast 1 task, how many ways the entrepenuer can assign those task to employees ?

Comments

Answer. 150

What i did (Please tell me where i am wrong ? )

 I have 3 employees and 5 jobs and everyone should get atleast one job

First lets provide everyone a job = C(5,1)*C(4,1)*C(3,1)  is the number of ways of assigning them jobs.

Now i have 2 jobs 3 employees any one can do any job so total = 3^2

Hence Answer = C(5,1)*C(4,1)*C(3,1)*3^2 = 540

Please tell me what is wrong here :(

Answer 1

Answer will be 150

Here it is given 5 different jobs has assigned to 3 different employee

So, number of ways will be

$A$       $B$       $C$

$3$        $1$      $1$

$1$        $3$      $1$

$1$        $1$      $3$

$2$        $2$      $1$

$2$.       $1$      $2$

$1$        $2$     $2$

So, no of ways we can give $5$ different job to $3$ different employee is $\left ( \binom{5}{3}\times \binom{2}{1} \times \binom{1}{1}\right )\times 3+\left ( \binom{5}{2}\times \binom{3}{2}\times \binom{1}{1} \right )\times 3=150$

Comments

Srestha where i  am doing wrong please point that out :)

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there is a small difference

ur ans is for "give 1 job to every employee first, then give 2 jobs to 3 employees"

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Srestha i understood but the statement  "give 1 job to every employee first, then give 2 jobs to 3 employees" and the statement asked in question both seems similar i cant understand the difference in both statement in question it says that number of ways so that every employee should have atleast one job and i also did accordingly so little bit confused here :(