How many Three digit numbers less than 600 can be formed from the digits: 2,3,5,6 & 8. W/ no repetitions allowed.
since our number has to be < 600, the lead digit can only be
2, 3, or 5
So we have 3 choices for the lead digit, one has been used up leaving 4 digits left for the middle and 3 digits for the unit digit
number of such numbers = 3 x 4 x 3 or 36 numbers
Thank you, I ended up figuring it out and finishing it that way so I'm glad I understood it the way it was explained, appreciate the response!
To find the number of three-digit numbers that can be formed using the digits 2, 3, 5, 6, and 8 with no repetitions allowed, we can follow these steps:
Step 1: Determine the possible choices for the hundreds place:
Since the number should be less than 600, the hundreds place can only be filled with the digit 2 or 3. Therefore, two choices are available.
Step 2: Determine the possible choices for the tens place:
After selecting a digit for the hundreds place, there are four digits remaining (excluding the one selected for the hundreds place). Therefore, four choices are available for the tens place.
Step 3: Determine the possible choices for the ones place:
After selecting digits for the hundreds and tens places, three digits remain. Therefore, three choices are available for the ones place.
Step 4: Multiply the number of choices for each place value together:
To calculate the total number of three-digit numbers, multiply the number of choices for each place value together:
Number of choices for hundreds place = 2
Number of choices for tens place = 4
Number of choices for ones place = 3
Total number of three-digit numbers = 2 x 4 x 3 = 24
Therefore, there are 24 three-digit numbers that can be formed from the digits 2, 3, 5, 6, and 8 with no repetitions allowed.
To find the number of three-digit numbers less than 600 that can be formed from the digits 2, 3, 5, 6, and 8, with no repetitions allowed, you can follow these steps:
Step 1: Determine the possibilities for the hundreds digit (first digit).
Since the number has to be less than 600, the hundreds digit can only be 2, 3, or 5 (because 6 or 8 as the hundreds digit would make the number greater than 600). Thus, we have 3 possibilities for the hundreds digit.
Step 2: Determine the possibilities for the tens digit (second digit).
Since no repetitions are allowed, we have 4 digits left (3, 5, 6, and 8) after using one in the hundreds place. Therefore, we have 4 possibilities for the tens digit.
Step 3: Determine the possibilities for the ones digit (third digit).
Again, no repetitions are allowed, so we have 3 digits left (3, 5, and 8) after using two in the hundreds and tens places. Thus, we have 3 possibilities for the ones digit.
Step 4: Multiply the number of possibilities for each digit together.
Multiply the number of possibilities for the hundreds, tens, and ones digits together: 3 x 4 x 3 = 36.
Therefore, there are 36 three-digit numbers less than 600 that can be formed from the digits 2, 3, 5, 6, and 8, with no repetitions allowed.