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:
Opción C, 30 días.
Step-by-step explanation:
Sabemos que:
Felipe asiste al cine cada 3 días
Miguel asiste cada 5 días.
Pedro asiste cada 6 días.
Los tres van juntos un día, ¿dentro de cuántos días irán otra vez juntos?
Los 3 volverán a ir juntos luego de N días, tal que N es el menor múltiplo común de 3, 5 y 6.
Como 6 es múltiplo de 3, podemos ignorar al 3, y solo considerar al menor múltiplo en común de 5 y 6.
Además, como podemos reescribir estos números como un producto de números primos, así obtenemos:
6 = 2*3
5 = 5*1
Estos números no comparten factores entre ellos, por lo que el menor múltiplo entre 5 y 6 es simplemente 5*6 = 30
Entonces podemos concluir que N = 30
Felipe, Pedro y Miguel irán juntos al cine nuevamente dentro de 30 días.
La opción correcta es C.
The length of the base is 32.6
3.3 + 3.3 = 6.6
Subtract 6.6 from 71.8 : 65.2
Divide that by 2 : 32.6
Answer:
35/20
Step-by-step explanation:
20 divided by 4 = 5
so our multiple is 5
5 x 4 = 20
so we have to do the same to the numerator
5 x 7 = 35
Simplified= 1 3/5
