Counting Combinations & Permutations with Repetition

In summary, the question is asking for the number of 6 digit numbers greater than 800,000 that can be made using the digits 1, 1, 5, 5, 5, and 8. The first digit must be 8 and the remaining digits can be arranged in (10) different ways. This information can be used to solve the problem.
  • #1
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I had mono while this unit was being taught so I am havin quite a lot of trouble figurin this homework out. Like this question:

How many 6 digit numbers greater than 800 000 can be made from the digits 1, 1, 5, 5, 5, 8?

I have absolutly no idea so any help would be appriciated! Thanks!
 
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  • #2
Format said:
I had mono while this unit was being taught so I am havin quite a lot of trouble figurin this homework out. Like this question:

How many 6 digit numbers greater than 800 000 can be made from the digits 1, 1, 5, 5, 5, 8?

I have absolutly no idea so any help would be appriciated! Thanks!
Because numbers must be greater than (800,000), the first digit must be 8. The number of different arrangements of the remaining 5 digits, consisting of 2-(1)'s and 3-(5)'s is given by:
{Number Arrangements} = (5!)/{(2!)*(3!)} = (10)


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  • #3
ah ok i was tryin something like that, but i didnt realize brackets were necessary. Thankyou!
 

FAQ: Counting Combinations & Permutations with Repetition

What is the difference between combinations and permutations?

Combinations and permutations are both ways to arrange objects, but the main difference is that permutations take into account the order of the objects while combinations do not. In other words, two permutations are considered different if the order of the objects is different, while two combinations with the same objects are considered the same regardless of their order.

How do you calculate the number of combinations or permutations?

The number of combinations can be calculated using the formula nCr = n! / (r! * (n-r)!), where n is the total number of objects and r is the number of objects being chosen. The number of permutations can be calculated using the formula nPr = n! / (n-r)!, where n is the total number of objects and r is the number of objects being chosen. It is important to note that n must be greater than or equal to r in both formulas.

When should I use combinations and when should I use permutations?

Combinations are used when the order of the objects does not matter, such as when choosing a group of people for a committee. Permutations are used when the order of the objects does matter, such as when arranging a sequence of events or selecting winners in a race.

Can combinations or permutations be repeated?

In most cases, combinations and permutations do not involve repetition of objects. However, there are variations such as with replacement, where an object can be chosen more than once, or with repetition, where the same object can appear multiple times in the arrangement.

How are combinations and permutations used in real life?

Combinations and permutations are used in various fields such as mathematics, statistics, computer science, and engineering. They can be used to solve problems involving probability, counting principles, and optimization. In real life, they can be applied to scenarios like lottery drawings, password combinations, and seating arrangements.

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