## anonymous 5 years ago A small start-up company with 16 employees will select its 4 board members from among the employees. How many different groups of board members are possible?

1. anonymous

now this is just the same as the previous one. you need $\dbinom{16}{4}$ do you know how to compute $\dbinom{n}{k}$ ?

2. anonymous

i dont think the last one was right lol it was actually some really large number

3. anonymous

well then it was because 'itinerary' meant the order mattered. so it was $10\times 9\times 8\times7=5040$

4. anonymous

yes! so then i do 16*15*14*13?

5. anonymous

but in this problem order does not matter, just who is selected. so this time it really is $\dbinom{16}{4}$

6. anonymous

Yes, you start out with 16*15*14*13 but this case is different because in this case you do not care in which order the people were picked. so you have do divide by the number of ways you can permute the 4 people, which is 4*3*2

7. anonymous

divide first, multiply last. $\dbinom{16}{4}=\frac{16 \times 15\times 14\times 13}{4 \times 3\times2}$

8. anonymous

1820?

9. anonymous

$=8\times 5\times 14\times 13$

10. anonymous

oops sorry

11. anonymous

2*5*14*13=1820

12. anonymous

you are right. i canceled incorrectly. sorry.

13. anonymous

no worries i just multiplied and then divided im lucky ahah

14. anonymous

that always works with a calculator. but the answer is always a whole number (because the question is "how many") so you can always cancel the entire denominator.

15. anonymous

Oh I see, thank you very mch!

16. anonymous

welcome.