How many five-digit even numbers, that are less than 5 and that are not divisible by 5, can be created from the digits 0, 1, 3, 5, 6, 7, 8 and 9, if no digit can be used more than once?

480 numbers

Step-by-step explanation:

We have to create a 5-digit even number less than 50,000 using the digits: 0, 1, 3, 5, 6, 7, 8 and 9

Total available digits = 8

No digit can be used more than once. We have to fill the 5 places using the 8 numbers.

Since, the number must be less than 50,000, the first digit cannot be 5 or greater than 5 and it cannot be 0 either. So there are only two possible choices for the 1st place i.e. either 1 or 3.

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Since the digit must be even and cannot be divisible by 5, so the last digit must be event but not 0. So there are 2 ways to fill the last place i.e. using 6 or 8.

2 possible ways , __ , __ , __ , 2 possible ways

When a digit is chosen for 1st and the last place, we will be left with 6 digits which can be chosen in any order. So, the 2nd place digit can be filled in 6 ways. After choosing this digit we are left with 5 digits.

Number of ways to fill the 3rd place = 5

Number of ways to fill the 4th place = 4

2 possible ways , 6 Possible ways , 5 Possible Ways , 4 Possible Ways , 2 possible ways

According to the fundamental counting principle, the number of total possible 5-digit numbers will be equal to the product of possibilities of each individual position.

i.e.

Total number of possible 5-digit numbers = 2 x 6 x 5 x 4 x 2 = 480

Therefore, 480 five-digit numbers can be formed using the given conditions.

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.