Answer:
20 people will ride each bus
Step-by-step explanation:
60 people, and 3 buses
you would divide 3 by 60
In plain and short, we simply divide 5 by (1+2+3) and then distribute the pieces likewise
![\bf 5\qquad 1:2:3\qquad \cfrac{5}{1+2+3}\implies \cfrac{5}{6} \\\\\\ \stackrel{\textit{ratio of 1}}{1\left( \frac{5}{6} \right)}\qquad \stackrel{\textit{ratio of 2}}{2\left( \frac{5}{6} \right)}\qquad \stackrel{\textit{ratio of 3}}{3\left( \frac{5}{6} \right)}\qquad \implies \qquad \frac{5}{6}~:~\frac{5}{3}~:~\frac{5}{2}](https://tex.z-dn.net/?f=%5Cbf%205%5Cqquad%201%3A2%3A3%5Cqquad%20%5Ccfrac%7B5%7D%7B1%2B2%2B3%7D%5Cimplies%20%5Ccfrac%7B5%7D%7B6%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Cstackrel%7B%5Ctextit%7Bratio%20of%201%7D%7D%7B1%5Cleft%28%20%5Cfrac%7B5%7D%7B6%7D%20%5Cright%29%7D%5Cqquad%20%5Cstackrel%7B%5Ctextit%7Bratio%20of%202%7D%7D%7B2%5Cleft%28%20%5Cfrac%7B5%7D%7B6%7D%20%5Cright%29%7D%5Cqquad%20%5Cstackrel%7B%5Ctextit%7Bratio%20of%203%7D%7D%7B3%5Cleft%28%20%5Cfrac%7B5%7D%7B6%7D%20%5Cright%29%7D%5Cqquad%20%5Cimplies%20%5Cqquad%20%5Cfrac%7B5%7D%7B6%7D~%3A~%5Cfrac%7B5%7D%7B3%7D~%3A~%5Cfrac%7B5%7D%7B2%7D)
add the ratios up, and you'll get 5.
Answer:
1716 ;
700 ;
1715 ;
658 ;
1254 ;
792
Step-by-step explanation:
Given that :
Number of members (n) = 13
a. How many ways can a group of seven be chosen to work on a project?
13C7:
Recall :
nCr = n! ÷ (n-r)! r!
13C7 = 13! ÷ (13 - 7)!7!
= 13! ÷ 6! 7!
(13*12*11*10*9*8*7!) ÷ 7! (6*5*4*3*2*1)
1235520 / 720
= 1716
b. Suppose seven team members are women and six are men.
Men = 6 ; women = 7
(i) How many groups of seven can be chosen that contain four women and three men?
(7C4) * (6C3)
Using calculator :
7C4 = 35
6C3 = 20
(35 * 20) = 700
(ii) How many groups of seven can be chosen that contain at least one man?
13C7 - 7C7
7C7 = only women
13C7 = 1716
7C7 = 1
1716 - 1 = 1715
(iii) How many groups of seven can be chosen that contain at most three women?
(6C4 * 7C3) + (6C5 * 7C2) + (6C6 * 7C1)
Using calculator :
(15 * 35) + (6 * 21) + (1 * 7)
525 + 126 + 7
= 658
c. Suppose two team members refuse to work together on projects. How many groups of seven can be chosen to work on a project?
(First in second out) + (second in first out) + (both out)
13 - 2 = 11
11C6 + 11C6 + 11C7
Using calculator :
462 + 462 + 330
= 1254
d. Suppose two team members insist on either working together or not at all on projects. How many groups of seven can be chosen to work on a project?
Number of ways with both in the group = 11C5
Number of ways with both out of the group = 11C7
11C5 + 11C7
462 + 330
= 792