Question

How many distinct 3 digit numbers can be written using the digits 4, 6 and 9 without

repeating the digits

a) What is the probability that the numbers are odd numbers?

b) What is the probability that the numbers are even numbers?​

Answer 1

Answer:

A three digit even number is to be formed from given 6 digits 1,2,3,4,6,7.

□□□

HTO

Since, for the number is to be even , so ones place can be filled by 2,4 or 6. So, there are 3 ways to fill ones place.

Since, repetition is not allowed , so tens place can be filled by remaining 5 digits. So, tens place can be filled in 5 ways.

Similarly, hundred's place can be filled by remaining 4 digits. So, hundred's place can be filled in 4 ways.

So,required number of ways in which three digit even numbers can be formed from the given digits is 4×5×3=60

Alternative Method:

3-digit even numbers are to be formed using the given six digits, ,2,3,4,6 and 7, without repeating the digits.

Then, units digits can be filled in 3 ways by any of the digits, 2,4 or 6.

Since the digits cannot be repeated in the 3-digit numbers and units place is already occupied with a digit (which is even), the hundreds and tens place is to be filled by the remaining 5 digits.

Therefore, the number of ways in which hundreds and tens place can be filled with the remaining 5 digits Is the permutation of 5 different digits taken 2 at a time.

5

P

2

=

(5−2)!

5!

=

3!

5!

Number of ways of filling hundreds and tens place

=

3!

5×4×3!

=20

Thus, by multiplication principle, the required number of 3-digit numbers is 3×20=60

Answer 2

Question:-

• How many distinct 3 digit numbers can be written using the digits 4, 6 and 9 without

• How many distinct 3 digit numbers can be written using the digits 4, 6 and 9 without repeating the digits?

a) What is the probability that the numbers are odd numbers?

a) What is the probability that the numbers are odd numbers?b) What is the probability that the numbers are even numbers?

Solution:-

• The number of distinct three digited number that can be written using 4 , 6 and 9 digits is ↓

= nPr (3,3)

= 6

( a ) Number of odd numbers that can be formed = 2

So, probability of getting an odd number

= 2/6

= 1/3

(b) Number of even numbers that can be formed = 4

So, probability of getting an even number

= 4 /6

= 2/3