Question

how many even numbers less than 1000 can be formed by using the digits 2,4,3 and 5 if repetition to the digits is allowed​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Concept:

If the selection consists of potentially nondistinct components (allowing repetitions), and the sequence in which the elements are selected counts, each element can be selected in different ways, regardless of the prior element selected.

Given:

The digits are 2, 4, 3, and 5.

Find:

How many even numbers less than 1000 can be formed by using the digits 2,4,3 and 5 if repetition to the digits is allowed​.

Solution:

The numbers that are less than 1000 that can be formed are of 1, 2 and 3 digits.

For even number the one's place can have the values 2 and 4 from the given numbers.

1 digit numbers:

These numbers will just have ones place.

∴ The numbers will be 2 and 4 only.

Total 1 digit even numbers possible = 2.

2 digits numbers:

These numbers will have ones and tens place.

Number of ways to fill ones place = 2

(∵ only 2 and 4 can be placed.)

Number of ways to fill tens place = 4

(∵ Repition is allowed.)

Total 2 digits even number possible $=4*2=8.$

3 digits numbers:

These numbers will have ones, tens and hundreds place.

Number of ways to fill ones place = 2

(∵ only 2 and 4 can be placed.)

Number of ways to fill tens place = 4

Number of ways to fill hundreds place = 4

(∵ Repition is allowed.)

Total 3 digits even number possible $=4*4*2=32.$

Total even numbers $< 1000=2+8+32=42.$

Hence 42 even numbers less than 1000 can be formed by using the digits 2,4,3 and 5 if repetition to the digits is allowed​.