How many numbers can be formed from the digits 1, 2, 3, 4 wh... | MATH - DEFINITION OF PERMUTATION, NUMBER OF PERMUTATIONS WITH OR WITHOUT REPETITION | SolveeIt | Solveeit

Today, August 20

Question

How many numbers can be formed from the digits 1, 2, 3, 4 when the repetition is not allowed.

A

$4P_{4}$

B

$4P_{3}$

C

$4P_{1} +^{4} ⥂ P_{2} +^{4} ⥂ P_{3}$

D

$4P_{1} +^{4} ⥂ P_{2} +^{4} ⥂ P_{3} +^{4} ⥂ P_{4}$

Answer

$4P_{1} +^{4} ⥂ P_{2} +^{4} ⥂ P_{3} +^{4} ⥂ P_{4}$

Explanation

Solution

Number of 1 digit numbers $=^{4} ⥂ P_{1}$

Number of 2 digit numbers $=^{4} ⥂ P_{2}$

Number of 3 digit numbers $=^{4} ⥂ P_{3}$

Number of 4 digit numbers $=^{4} ⥂ P_{4}$

Hence the required number of ways

$=^{4} ⥂ P_{1} +^{4} ⥂ P_{2} +^{4} ⥂ P_{3} +^{4} ⥂ P_{4}$ .