# In how many ways? Checking my answers

A computer monitor manufacturer produces 7 different models, all with a different selling price. Suppose that 4 different customers (call them A, B, C and D) will each purchase one of the monitors.

I just want to check my answers. If this is right or wrong.

In how many ways may this be done assuming that no two customers purchase the same model?

I did a sample space here. i assume that no two customers purchase the same model so i did like this . Customer A can purchase 7 different models. B can purchase 6 different models. C can purchase 5 different models. D can purchase 4 different models. Multiply them then i got 840 ways to do it.

In how many ways may this be done assuming that different customers may purchase the same model?

For this one, I got 5040 ways to do it because I 7!.? i honestly i am confuse in this part.

• Same reasoning as before. First customer has $7$ choices, so does the second, and so on. Hence $7^4=2401$ – lulu Sep 15 '16 at 1:28
• $7!$ is wrong. $A$ can purchase any one of seven models, $B$ can purchase any one of seven models,$C$ can purchase any one of seven models,and $D$ can purchase any one of seven models. So the answer is $7*7*7*7=2401$. – астон вілла олоф мэллбэрг Sep 15 '16 at 1:30
• I really thank you guys for explaining it to me very well! – Tenji Kiriyama Sep 15 '16 at 1:45

## 1 Answer

Yes, I believe you are correct. For those saying it is incorrect, note that Tenji says

...assuming no two customers purchase the same model...

Also, the reason you got 5040 is that $7!$ is actually $7*6*5*4*3*2*1$, whereas you wanted $7*6*5*4$.

• actually the part where ...assuming no two customers purchase the same model... is the 7 * 6 * 5 * 4 = 840 ways and actually got that answer before posting here... what i dont get and they answered is the question: In how many ways may this be done assuming that different customers may purchase the same model? they answered 2401 – Tenji Kiriyama Sep 15 '16 at 1:42
• ah. never mind then. anyway, did the explanation about the factorial error help at all? lol – TrojanByAccident Sep 15 '16 at 2:09
• They did and it make sense! I also thank you for trying to help me! Combinations and permutations word problems really confuse me. – Tenji Kiriyama Sep 15 '16 at 2:16
• :D No problem! They can be quite confusing at first. – TrojanByAccident Sep 15 '16 at 2:27