Question

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

Answer 1

Answer:

A. 1562 numbers , B. 130 numbers

Step-by-step 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