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*2* 1=6\\eq 120.`

So, option (A) is incorrect.

Option (B) : If n = 4, then

`n!=4!=4* 3*2* 1=24\\eq 120.`

So, option (B) is incorrect.

Option (C) : If n = 5, then

`n!=5!=5*4*3*2* 1=120.`

So, option (C) is correct.

Option (D) : If n = 6, then

`n!=6!=6*5* 4*3*2*1=720\\eq 120.`

So, option (D) is incorrect.

Thus, (C) is the correct option.