Question

How many four digit numbers can be formed using the digits 3,4,0,1 only once in a number

Answer 1

Step-by-step explanation:

• Total there are 4 digits, from which we have to form 4 digits number.
• We need to choose 4 digits randomly and form a number without repeating any digit.
• In this process, we need to determine the number of possibilities where order does not matter.

So, we use the permutation formula and that is

$^{n}{P} _{r} = \frac{n ! }{(n - r) ! }$

where n is the total number of objects and r is the number of objects taken at a time.

Given:

• n = 4 and r = 4

$∴ \: \: ^{4}{P} _{4} = \frac{4 ! }{(4- 4) ! }$

$= \frac{4 ! }{0 ! } = 4! = 4 \times 3 \times 2 \times 1 = 24$

$∴ \: \: ^{4}{P} _{4} = 24$

∴ In 24 ways the 4-digits numbers can be form using the digits 3,4,0,1