Question

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

• A. ${}^4{P}_4$
• B. ${}^4{P}_3$
• C. ${}^4{P}_1{+}^4{P}_2{+}^4{P}_3$
• D. ${}^4{P}_1{+}^4{P}_2{+}^4{P}_3{+}^4{P}_4$

Answer 1

The correct option is D ${}^4{P}_1{+}^4{P}_2{+}^4{P}_3{+}^4{P}_4$

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
${}^4{P}_1{+}^4{P}_2{+}^4{P}_3{+}^4{P}_4$