Question

How many even k-digit numbers can be constructed out of the digits 3, 4, 5, 6, and 7?

a. Assume first that you may use the same digit again.
b. Assume that you cannot use a digit more than once.

Answer 1

A. 1562 numbers , B. 130 numbers

Explanation:

A) Using same digit again

1 digit nos = 2 ( ie 4 , 6 )

2 digit nos = 5 (ie any no) x 2 ( ie 4 ,6 )

Similarly

3 digit nos = 5 x 5 x 2

4 digit nos = 5 x 5 x 5 x 2

5 digit nos = 5 x 5 x 5 x 5 x 2

Adding all 5 equations

Total = 2 + 10 + 50 + 250 + 1250 = 1562

B) Cant use a digit more than once

1 digit nos = 2 ( ie 4 , 6 )

2 digit nos = 4 ( ie any no other than 4 or 6) x 2 ( ie 4 , 6 )

Similarly

3 digit nos = 4 x 3 x 2

4 digit nos = 4 x 3 x 2 x 2

5 digit nos = 4 x 3 x 2 x 1 x 2

Adding all five equations

Total = 2 + 8 + 24 + 48 + 48 = 130