Question

There are $4$ boys and $3$ girls. Arrange the following in ascending order.
a. Number of ways to arrange them in a row
b. Number of ways to arrange them around a table
c. Number of ways to arrange them in a row such that no two girls are together.
d. Number of ways to arrange them around at a table such that all $3$ girls are together

• A. d, c, b, a
• B. d, b, c, a
• C. a, b, c, d
• D. a, c, b, d

Answer 1

The correct option is B d, b, c, a

There are $4$ boys and $3$ girls
a) Number of ways arranging them in row is $(4+3)!=7!=5040$
b) Number of ways arranging them around a table is $(4+3-1)!=6!=720$
c) Number of ways to arrange them in a row such that no two girls are together is $4!$ is for arrangement of boys now we have $5$ place left adjacent to boys for girls but out of $5$ we need to select only $3$ for girls
$4!\times 5_{C_3}\times 3!=2400$
d) Number of ways of arranging them around a table such that all $3$ girls are together.
In this we will put all the girls in one unit, so we will have $5$ things to arrange around a table($4$ boys $+1$ unit of $3$ girls)
$=4!\times 3!=144$
So ascending order is d,b,c,a