There are 15 technicians and 11 chemists working in a research laboratory. In how many ways could they form a 5-member safety committee if the committee

a) may be chosen in any way?
b)must have exactly one techinician?
c)must have exactly one chemist?
d)must have exactly two chemists?
e)may be all technicians or all chemists?

I need help solving these questions.. it confuses me
Any help will be greatly appreciated. Thanks

There are 15 technicians and 11 chemists working in a research laboratory. In how many ways could they form a 5-member safety committee if the committee

[quote]a) may be chosen in any way?

In this case, we are just choosing 5 from 26.


b)must have exactly one technician?

Choose 1 from the 15 technicians and 4 from the 11 chemists.

C(15,1)C(11,4)


c)must have exactly one chemist?

Similar to #2



d)must have exactly two chemists?

Similar to #2 except use 2 instead of 1.


e)may be all technicians or all chemists?

Choose 5 chemists or 5 technicians:

C(15,5)+C(11,5)

[QUOTE=lisanoce;1717355]There are 15 technicians and 11 chemists working in a research laboratory. In how many ways could they form a 5-member safety committee if the committee



In this case, we are just choosing 5 from 26.



Choose 1 from the 15 technicians and 4 from the 11 chemists.

C(15,1)C(11,4)



similar to #2




similar to #2 except use 2 instead of 1.



choose 5 chemists or 5 technicians:

C(15,5)+C(11,5)



Thanks so much! I have one more combinations question. I did the first one but I don't understand the rest.

1) Jeffrey, a DJ at a local radio station, is choosing the music he will play on his shift. He must choose all his music from the top 100 songs for the week and he must play at least 12 songs an hour. In his first hour, all his choices must be from the top- 20 list.

a) In how many ways can Jeffrey choose the songs for his first hour if he wants to choose exactly 12 songs?

the answer I got was 20C12 = 125970 right?

b) In how many ways can Jeffrey choose the 12 songs if he wants to pick 8 of the top 10 and 4 from the songs listed from 11 to 20 on the chart?

c)In how many ways can Jeffrey choose either 12 or 13 songs to play in the first hour of his shift?

d)In how many ways can Jeffrey choose the songs if he wants to play up to 15 songs in the first hour?

Answers:

b) 9450
c) 203 490
d) 257 754

[QUOTE=galactus;1717388]



Thanks so much! I have one more combinations question. I did the first one but i don't understand the rest.

[quote]1) Jeffrey, a DJ at a local radio station, is choosing the music he will play on his shift. He must choose all his music from the top 100 songs for the week and he must play at least 12 songs an hour. In his first hour, all his choices must be from the top- 20 list.


a) In how many ways can Jeffrey choose the songs for his first hour if he wants to choose exactly 12 songs?

the answer i got was 20C12 = 125970 right?

Yep.


b) In how many ways can Jeffrey choose the 12 songs if he wants to pick 8 of the top 10 and 4 from the songs listed from 11 to 20 on the chart?

He has to choose 8 from 10 and 4 from 10. C(10,8)C(10,4)


c)In how many ways can Jeffrey choose either 12 or 13 songs to play in the first hour of his shift?

When it is OR, you can add them instead of multiplying. See why? They are independent.

C(20,13)+C(20,12)


d)In how many ways can Jeffrey choose the songs if he wants to play up to 15 songs in the first hour?

Remember, he must play at least 12. So, he plays at least 12 but up to 15.

\sum_{k=12}^{15}C(20,k)=C(20,12)+C(20,13)+C(20,14) +C(20,15)