A zoo has a menagerie containing four pairs of different animals, one male and one female for each. The zookeeper wishes to feed the animals in a specific pattern: each time he feeds a single animal, the next one he feeds must be a different gender. If he starts by feeding the male giraffe, how many ways can he feed all the animals?

Question

contestada

Respuesta :

akiran007 akiran007 · Answer 1 · 2020-07-20T04:58:57+02:00

Answer:

144

Step-by-step explanation:

We will use permutations to solve this problem

There are 4 pairs each having a male and a female.

The total number of sample points is 4! = 4*3*2*1= 24

He chooses the male first then the number of sample space he is left with are 3! = 3*2*1=6

The total number of ways he can select is 4! 3! = 24 * 6= 144

Another way of finding it out is

he has 4 pairs each having a male and a female so he chooses 1st male then he would choose from this

4 female choices*3 male choices * 3 female choices *2 male choices *2 female choices *1 male choices *1 female choices *= 4*3*3*2*2*1*1= 144

MrRoyal MrRoyal · Answer 2 · 2021-12-30T17:59:19+01:00

The zookeeper can feed all the animals in 144 ways

The number of different animals is given as:

[tex]n = 4[/tex]

The number of ways to feed any of the 4 male animals is:

[tex]Ways = 4![/tex]

Expand

[tex]Ways = 4 \times 3 \times 2 \times 1[/tex]

[tex]Ways = 24[/tex]

From the question, we understand that the female of the particular animal cannot be selected (yet).

So, there are 3 female animals left.

The number of ways to feed any of the 3 female animals is:

[tex]Ways = 3![/tex]

Expand

[tex]Ways = 3 \times 2 \times 1[/tex]

[tex]Ways = 6[/tex]

So, the number (n) of ways to feed all the animals is:

[tex]n = 24 \times 6[/tex]

[tex]n = 144[/tex]

Hence, he can feed all the animals in 144 ways