Respuesta :
Answer:
(a) 350
(b) 175
(c) 21
(d) 196
Step-by-step explanation:
Number of females = 7
Number of males = 5
Total ways of selecting r items from n items is
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
(a)
Total ways of selecting 3 females and 2 males.
[tex]\text{Total ways}=^7C_3\times ^5C_2[/tex]
[tex]\text{Total ways}=\dfrac{7!}{3!(7-3)!}\times \dfrac{5!}{2!(5-2)!}[/tex]
[tex]\text{Total ways}=35\times 10[/tex]
[tex]\text{Total ways}=350[/tex]
(b)
Total ways of selecting 4 females and 1 male.
[tex]\text{Total ways}=^7C_4\times ^5C_1[/tex]
[tex]\text{Total ways}=32\times 5[/tex]
[tex]\text{Total ways}=175[/tex]
(c)
Total ways of selecting 5 females.
[tex]\text{Total ways}=^7C_5\times ^5C_0[/tex]
[tex]\text{Total ways}=21\times 1[/tex]
[tex]\text{Total ways}=21[/tex]
(d)
Total ways of selecting at least 4 females.
Total ways = 4 females + 5 females
[tex]\text{Total ways}=175+21[/tex]
[tex]\text{Total ways}=196[/tex]
