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algol [13]
2 years ago
11

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

Mathematics
2 answers:
Mademuasel [1]2 years ago
8 0
C........................
faust18 [17]2 years ago
4 0

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

<u><em>Option (A)</em></u> :  If n = 3, then

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

So, option (A) is incorrect.

<u><em>Option (B)</em></u> :  If n = 4, then

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

So, option (B) is incorrect.

<u><em>Option (C)</em></u> :  If n = 5, then

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

So, option (C) is correct.

<u><em>Option (D) </em></u>:  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.

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