The number of three digit or four digit even numbers that can be formed from the numbers 2, 3, 5, 7 is
A.72
B.120
C.144
D.5040
Question:
Can digits be repeated,
e.g. is 332 allowed as a 3 digit number?
both groups must end with a "2"
I will assume digits may repeat
number of 3 digit even numbers = 4x4x1 = 16
number of 4 digit even numbers = 4x4x4x1 = 64
total = 80
mmhhh?
suppose we can't repeat
3digit evens = 3x2x1
= 6
4digit evens = 3x2x1x1 = 6
that would be only 12 total
something is not right with your choices.
Am I reading the question correctly?
Reiny I just realized "even meter" means not repeated.
That help????
Reiny I just realized "even numbers" means not repeated.
That help????
To find the number of three-digit or four-digit even numbers that can be formed from the numbers 2, 3, 5, and 7, we need to consider a few conditions:
1. The last digit must be even, which means it can only be 2 or 6.
2. The first digit cannot be zero.
Now let's break down the problem into two cases:
Case 1: Four-digit numbers:
If we consider four-digit numbers, then the first digit can be any of the numbers 2, 3, 5, or 7. After choosing the first digit, the second and third digits can be any of the four numbers. Finally, the last digit must be even, which means it can only be 2 or 6. Therefore, we have:
4 choices for the first digit × 4 choices for the second digit × 4 choices for the third digit × 2 choices for the last digit = 4 × 4 × 4 × 2 = 128
Case 2: Three-digit numbers:
If we consider three-digit numbers, then the first digit can be any of the numbers 2, 3, 5, or 7. After choosing the first digit, the second digit can be any of the four numbers, and the last digit must be even, which means it can only be 2 or 6. Therefore, we have:
4 choices for the first digit × 4 choices for the second digit × 2 choices for the last digit = 4 × 4 × 2 = 32
Now, to get the final answer, we add the number of four-digit numbers and three-digit numbers together:
128 + 32 = 160
Therefore, the correct answer is not listed among the given options.