How many numbers of not more than 4 digits can be formed with the digits , 2, 3 and 4, repetitions being allowed ?

 

  1  How many numbers of not more than 4 digits can be formed with the digits ,   2, 3 and 4,  repetitions being allowed ?

Solution:-

Satisfying the restriction imposed in the problem we can form 1-digit or 2-digit or 3-digit or 4-digit numbers. digits occupy To find the no. of 1-digit numbers, we note that, 4 different digits are given; so, the no. of 1 -digit numbers is 4.

To find the no. of 2-digit numbers we note that the unit's place can be filled up in 4 ways, for any one of the 4 different digits can be placed there. For each of these 4 ways the ten's place can also be filled up in 4 ways as repetition of digit  

is allowed.

 the no. of 2-digit numbers = 4.4 = 42 = 16. Arguing in the same way we have, no. of 3-digit numbers = 43 = 64 and no. of 4-digit numbers = 4⁴ = 256.

Hence, the required no. of numbers = 4+ 16+64 +256 = 340.