In how many ways can five children stand in a queue?

1.	In how many ways can five children stand in a queue?
Answer» The number of arrangements of ‘n’ things taken all at a time = P (n, n) Therefore by using the formula, On using the formula, P (n, r) = n!/(n – r)! Total number of ways in which five children can stand in a queue = the number of arrangements of 5 things taken all at a time = P (5, 5) Therefore, P (5, 5) = 5!/(5 – 5)! = 5!/0! = 5! [Since, 0! = 1] = 5 × 4 × 3 × 2 × 1 = 120 Thus, number of ways in which five children can stand in a queue are 120.

Answer»

The number of arrangements of ‘n’ things taken all at a time = P (n, n)

Therefore by using the formula,

On using the formula,

P (n, r) = n!/(n – r)!

Total number of ways in which five children can stand in a queue = the number of arrangements of 5 things taken all at a time = P (5, 5)

Therefore,

P (5, 5) = 5!/(5 – 5)!

= 5!/0!

= 5! [Since, 0! = 1]

= 5 × 4 × 3 × 2 × 1

= 120

Thus, number of ways in which five children can stand in a queue are 120.

Discussion