Question

Five boys and five girls want to sit in a row .In how many ways can they sit such that no two boys sit together? Select one:

a. 6(5!)^2

b. 6!X5!

c.

a.720

d. 2x6x5!

Answer 1

the answer is

D) 2*6*5

Answer 2

Answer: Option 'a' is correct.

Step-by-step explanation:

Since we have given that

Number of boys = 5

Number of girls = 5

According to question, no two boys sit together,

So, pattern would be

BGBGBGBGBG

or

GBGBGBGBGB

So, number of gaps between 5 girls is 6

but the number of boys are only 5.

So, $^6C_5=6$

So, the number of ways that no two boys sit together is given by

$6\times 5!\times 5!\\\\=6\times (5!)^2$

Hence, Option 'a' is correct.