Question

If a group of distinct objects can be arranged in 120 different ways, how many objects are there? A. 3 B. 4 C. 5 D. 6

Answer 1

C........................

Answer 2

Answer:  The correct option is (C) 5.

Step-by-step explanation:  Given that a group of distinct objects can be arranged in 120 different ways.

We are to find the number of objects in the group.

We know that a group of n distinct objects can be arranged in n! ways.

And, for a non-negative integer n, the factorial of n is defined as

$n!=n(n-1)(n-2)~~.~~.~~.~~3.2.1$

Option (A) :  If n = 3, then

$n!=3!=3\times2\times 1=6\neq 120.$

So, option (A) is incorrect.

Option (B) :  If n = 4, then

$n!=4!=4\times 3\times2\times 1=24\neq 120.$

So, option (B) is incorrect.

Option (C) :  If n = 5, then

$n!=5!=5\times4\times3\times2\times 1=120.$

So, option (C) is correct.

Option (D) :  If n = 6, then

$n!=6!=6\times5\times 4\times3\times2\times1=720\neq 120.$

So, option (D) is incorrect.

Thus, (C) is the correct option.