NCERT Class XI Mathematics - Permutations and Combinations - Solutions
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Question : 14
Total: 41
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?
Solution:
The 4-digit numbers can be formed from digits 1 to 5 in
P 4
∴ The required 4 digit numbers =
P 4
For 4-digit even numbers unit place can be filled by 2, 4, i.e., in 2 ways.
Then the remaining three places can be filled in
P 3
∴ The required 4-digit even numbers = 2 ×
P 3
∴ The required 4 digit numbers =
For 4-digit even numbers unit place can be filled by 2, 4, i.e., in 2 ways.
Then the remaining three places can be filled in
∴ The required 4-digit even numbers = 2 ×
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