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
Answer: 0 months its already shorter than hanks tree
They are the same , hope this helps :)
Answer:
Hope this helps :)
Step-by-step explanation:
15
(3^5)÷(3^5)
Simplify 3^5
243÷243
1
(3^5)÷(3^5)
3^5/3^5=3^5-5
3^5-5
3^5-5= 1
1
Formula: x^a/x^b=x^a-b
16
2^10/2^10
Cancel out 2^10
1
2^10/2^10
2^10/2^10=2^10-10
2^10-10
2^10-10=1
1
Formula: x^a/x^b=x^a-b
17
x^7/x^7x≠0
x≠0
18
(4x+2y)5÷(4x+2y)^5(4x+2y) ≠ 0
5/(4x+2y)^3 ≠ 0
5 ≠ 0
≠ =-y/2
19
No solution
20
p^4/p^4p ≠ 0
p≠ 0
no solution
Answer:
69
Step-by-step explanation:
