Question

Jones and North, a stock brokerage firm, has received five different inquiries regarding new accounts. In how many different ways can these five inquiries be assigned to ts four account executives such that each inquiry is handled by one account executive and no account executive handles more than two inquiries?

Answer 1

i think we can reason this out
5 choices for first exec, 4 for second 3 for third 2 for fourth, and then they all have one so the last can go to any of the 4. so it looks like (without using a fancy formula) the answer should be
\[5\times 4\times 3\times 2\times 5\]

Answer 2

well that last part was a typo i should be
\[5\times 4\times 3\times 2\times 4\]

Answer 3

The answer is 600. They used combination and factorial.

Answer 4

does this look reasonable?

Answer 5

hmm then first answer was right, not second one

Answer 6

i'd love to know why...

Answer 7

me too.

Answer 8

I see it is possible for an executive to have 0 inquiries.

Answer 9

This is then: five letter strings using a,b,c,d but none more than twice.
e.g: aabbc, aabbd, aabcc, aabcd, aabdd, aaccd...

Answer 10

So solve it as two problems: Number of ways to have one repeating, plus number of ways to have two repeating.

Answer 11

Number of ways to have one repeating is 4 * 5!/2 = 240 because there are 4 execs you could pick to have the double draw, and once you've picked that 5! ways to arrange the inquiries (but divide by two because for the double duty exec the order of the two inquiries doesn't matter).

Answer 12

How many ways can you re-arrange 'aabbc'? 5!/(2!*2!) = 30.
How many ways can you pick one Account Exec to get zero and one exec to get exactly one? 4*3 = 12. So total = 12*30 = 360. 360+240 = 600.