Find how many six-digit numbers can be formed from the digits 2, 3, 4, 5, 6 and 7 (with repetitions), if:
the numbers formed must be divisible by 25
Oops again
25 and 75 are both allowed, so 6^4 * 2
Oops. Go with R_Scott. I neglected to omit 0 as a choice.
yup ... 75 is included ... thanks, oobleck
To find the number of six-digit numbers that can be formed from the digits 2, 3, 4, 5, 6, and 7, with the condition that they must be divisible by 25, we need to consider two things:
1. The last two digits of the number must be either 25, 50, 75, or 00, as these are the only combinations that would make the number divisible by 25.
2. The first four digits can be any of the given digits (2, 3, 4, 5, 6, and 7), including repetitions.
Let's break down the problem step by step to find the solution:
Step 1: Count the options for the last two digits.
There are four options for the last two digits: 25, 50, 75, and 00.
Step 2: Count the options for the first four digits.
Since we can use the digits 2, 3, 4, 5, 6, and 7 (with repetitions), each of the four digits can be any of these six options. Therefore, there are 6 options for each of the four digits. Since the digits can be repeated, each digit can be chosen independently.
To find the total number of options for the first four digits, we need to multiply the number of options for each digit together:
6 (options for the first digit) * 6 (options for the second digit) * 6 (options for the third digit) * 6 (options for the fourth digit) = 6^4 = 1296.
Step 3: Calculate the total number of possibilities.
To get the total number of six-digit numbers, we need to multiply the number of options for the last two digits by the number of options for the first four digits:
4 (options for the last two digits) * 1296 (options for the first four digits) = 5184.
Therefore, there are 5184 six-digit numbers that can be formed using the digits 2, 3, 4, 5, 6, and 7, with the condition that they must be divisible by 25.
6^4
the 1st four digits can be any of the six , the last two must be 2 5
must end in 25, 50, 75 or 00
6^4 * 4