How many different 4-digit even numbers can be formed from the digits 1, 3, 5, 6, 8, and 9 if no repetition of digits is allowed?

General
1

how many different 4-digit even numbers can be formed from the digits 1, 3, 5, 6, 8, and 9 if no repetition of digits is allowed?

2

How many different 4-digit even numbers can be formed from the digits 1, 3, 5, 6, 8, and 9 if no repetition of digits is allowed?

Answer:
To determine the number of different 4-digit even numbers that can be formed from the digits 1, 3, 5, 6, 8, and 9 without repetition of digits, we need to consider the following steps:

Solution By Steps:

1. Identify Possible Digits for the Units Place:

Since the number must be even, the units place must be occupied by one of the even digits available: 6 or 8 (because we are not allowed to repeat digits and these are the only even digits in the list).

2. Calculate Combinations for Each Case of the Units Place:

Case 1: Units place = 6

  • If the units place is occupied by 6, we have the digits {1, 3, 5, 8, 9} remaining for the thousands, hundreds, and tens places.
  • Since we need to form a 4-digit number, let’s proceed to count the possible combinations.

  1. Thousands place:

    • We have 5 digits to choose from.

  2. Hundreds place:

    • We have 4 remaining digits to choose from after filling the thousands place.

  3. Tens place:

    • We have 3 remaining digits to choose from after filling the hundreds place.

Therefore, the number of possible combinations when the units digit is 6 is:

5 \times 4 \times 3 = 60

Case 2: Units place = 8

  • If the units place is occupied by 8, we have the digits {1, 3, 5, 6, 9} remaining for the thousands, hundreds, and tens places.
  • Similar to the previous case:

  1. Thousands place:

    • We again have 5 digits to choose from.

  2. Hundreds place:

    • We have 4 remaining digits to choose from after filling the thousands place.

  3. Tens place:

    • We have 3 remaining digits to choose from after filling the hundreds place.

Therefore, the number of possible combinations when the units digit is 8 is:

5 \times 4 \times 3 = 60

3. Calculate the Total Number of Combinations:

Since both scenarios result in 60 possible combinations, the total number of different 4-digit even numbers that can be formed is:

60 + 60 = 120

Final Answer:
The number of different 4-digit even numbers that can be formed from the given digits is \boxed{120}.