Question

How many positive odd integers less than 10,000 can be written using the digits 3, 4, 6, 8, and 0 if repeating the digits are allowed? A.100 B. 125 C. 150

Answer 1

olution:

Recall the Fundamental Counting principle; if there are m ways to make a selection and n ways to make a second selection, then there are m x n number of ways in which two selection can be made.

ut of the provided digits, if the number ends with 3

ase 1: Tnumber of one digit numbers.

ut of the digits provided, only one way to fil;l the box that is with one.

Thus, there is one digit odd integer here.

Case 2: The number of two digits.

Out of the digits provided, only one way to fill the last box is with digit 3, and any one of the 4 digits can filled in it as 0 cannot filled in either of the box.

Thus, number of ways are;

`4*1=4`

Aase 3: The number of three digit numbers.

ut of the digits provided, only one way to flll the last box is with digit 3, and any one of the 5 digits can be filled in second box, and thus any one of the 4 digits can be filled in first box as 0 cannot be fixed in the box.

Thus, number of ways are;

`4*5*1=20`

Lastly;

: The numbver of four digit numbers.

he number of ways are;

`4*5*5*1=100`

Thus, the total number of ways to select are;

`100+20+4+1=125`

INAL ANSWER: 125