How many 5-digit odd numbers can be made using the digits 3, 5, 6, 7 and 9, if digits cannot be repeated?
There are only 4 ways to choose the final digit, since it must be an odd number. After that one is chosen, any unused digits may be selected in the other places. So, selecting the digits right-to-left, there are
4*4*3*2*1 = 96 ways to choose the digits.
if the digits 1,3,5.7,9, what is the different
if all the digits are odd, then there are 5 choices for the last digit. So, the number of choices changes to
5*4*3*2*1 = 120
was that not immediately clear?
If digits cannot be repeated,how many three digit numbers can be made using the digits 3, 5, 7 and 9 ?
I know if four digit using the digit 3,5,7,and 9 , the answer is 4*3*2*1=24,
but if three digit using the digit 3, 5,7, and 9, the answer is 3*2*1=6?
no; there are 4 choices for the 1st digit, then 3, then 2, so
4*3*2 = 24
Start with the greatest number of choices and work down. You don't have to end at 1.
A 3-digit number using the digits 1,3,5,7,9 would have 5*4*3 = 60 ways.
To find the number of 5-digit odd numbers that can be made using the given digits without repetition, we need to break down the problem step by step.
Step 1: Determine the options for the thousands place.
Since the number must be odd, the thousands place cannot be 6. So, we have 4 options for the thousands place: 3, 5, 7, and 9.
Step 2: Determine the options for the units place.
Since the number must be odd, the units place has to be either 3, 5, 7, or 9. However, since we cannot repeat digits, we have only 3 options for the units place after using one of the digits as the thousands place.
Step 3: Determine the options for the hundreds, tens, and thousands places.
Now, we have only three remaining digits: 3, 5, and 7. Since we cannot repeat digits, we have only 3 options for the hundreds place, 2 options for the tens place, and 1 option for the thousands place.
Step 4: Calculate the total number of possibilities.
To find the total number of 5-digit odd numbers, we multiply the number of options at each place value: 4 (thousands place) × 3 (hundreds place) × 2 (tens place) × 3 (units place) × 1 (units place again).
4 × 3 × 2 × 3 × 1 = 72
Therefore, there are 72 different 5-digit odd numbers that can be made using the digits 3, 5, 6, 7, and 9 without repetition.