Math, asked by amdsamir878, 1 month ago

Of the numbers formed by using all the figures 1, 2, 3, 4, 5 only once, how many are even?​

Answers

Answered by DV75308
1

Answer:

48

Step-by-step explanation:

Of the numbers formed using 1,2,3,4,5 only once, the numbers that have either 2 or 4 in their ones place will be even numbers.

If we consider numbers ending with 2, then four digits 1,3,4,5 can be used before 2. The number of 4-digit numbers that can be written using 1,3,4,5 only once is 4!=24" role="presentation" style="display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">4!=244!=24. Similarly, the number of 4-digit numbers that can be written using 1,2,3,5 only once (because this time the numbers end with 4) is again 24.

Hence, of the numbers formed by using all the figures 1,2,3,4 and 5 only once, 24+24=48 are even.

Answered by GulabLachman
4

Given: The numbers are formed using the digits 1,2,3,4 and 5 only once.

To find: Number of even numbers out of them

Explanation: For the number to be even, the number should end with an even digit. Out of these 5 numbers, only 2 or 4 are even. Therefore, the last digit can end with any of these 2 digits.

The last digit can be filled in 2 ways. The other 4 digits can be filled in any order in four places.

Total ways to arrange these 4 places= 4!

Total numbers formed

= 4! ×2

= 24×2

= 48 ways

Therefore, there are 48 even numbers that can be formed using 1,2,3,4 and 5 only once.

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