Question

How many 3-digit numbers can be formed with the digits 1,4,7,8 and 9 if the digits are not repeated ?

A) 60 B) 26 C) 50 D) 64

Answer 1

Answer:

5P3 = 5!/(5-3)! = 5!/2!

= 5×4×3×2×1/2×1

= 60

Answer 2

60, 3-digits numbers are formed from the given digits without repetition.

Option A is correct.

Given

• Digits 1,4,7,8 and 9.

To find:

• How many 3-digit numbers can be formed with the digits 1,4,7,8 and 9 if the digits are not repeated ?

• A) 60
• B) 26
• C) 50
• D) 64

Solution:

Concept to be used:

If out of n objects, r objects are choosen without repetition, then number of arrangements are

$\bf ^nP_r=\frac{n!}{(n-r)!}$

Step 1:

Write the terms used for permutation.

Digits given: 1,4,7,8, and 9

$\bf n = 5$

3-digit number to be formed, so

$\bf r = 3$

Step 2:

Write the number formed.

3-digit numbers formed by given digits are

$^5P_3=\frac{5!}{(5 - 3)!}$

$^5P_3=\frac{5!}{2!}$

$^5P_3=\frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1}$

$\bf ^5P_3=60$

Thus,

60, 3-digits numbers are formed from the given digits without repetition.

Option A is correct.

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