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
Solutions
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 agoRelated Solutions
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