Question

In: Statistics and Probability

How many ways can you arrange 5 boys and 6 girls alternately in a row of...

How many ways can you arrange 5 boys and 6 girls alternately in a row of 12 seats? An empty seat between 2 boys is not allowed. As it is so for 2 girls.

The choices given are:

a. 86,400

b. 345,600

c. 691,200

d. 1,036,800

e. 2,764,800

Expert Solution

B = total number of boys = 6

G = Number of girls = 5

To arrange the 6 boys and 5 girls alternatively in a row of 12 seat in such way that there is no empty seat between 2 boys and girls

Possible arrangements are

Possible Cases

Arrangement of 12 seat

1

X

B

G

B

G

B

G

B

G

B

G

B

2

B

X

G

B

G

B

G

B

G

B

G

B

3

B

G

X

B

G

B

G

B

G

B

G

B

4

B

G

B

X

G

B

G

B

G

B

G

B

5

B

G

B

G

X

B

G

B

G

B

G

B

6

B

G

B

G

B

X

G

B

G

B

G

B

7

B

G

B

G

B

G

X

B

G

B

G

B

8

B

G

B

G

B

G

B

X

G

B

G

B

9

B

G

B

G

B

G

B

G

X

B

G

B

10

B

G

B

G

B

G

B

G

B

X

G

B

11

B

G

B

G

B

G

B

G

B

G

X

B

12

B

G

B

G

B

G

B

G

B

G

B

X

X : Empty seat

for each cases 6 boys and 5 girls can be arranged in ⁶P₆ * ⁵P₅ ways

Hence total number of ways = 12 * ⁶P₆ * ⁵P₅ = ^1036800

Correct Answer: d = 1036800.

orchestra answered 1 year ago

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