Permutations with Indistinguishable Items

The video tutorial explains how to calculate the number of distinguishable permutations of a set of letters, some of which are repeated. It introduces the concept of indistinguishable items and provides a formula to calculate permutations by dividing the factorial of the total number of items by the product of the factorials of the repeated items. An example is worked through step-by-step, and the result is verified using a calculator.

What is the main reason for having fewer permutations when some letters are repeated?

• The number of letters is too small.

• Repeated letters are indistinguishable.

• Repeated letters are distinguishable.

• All letters are unique.

Which formula is used to calculate permutations of objects with indistinguishable items?

• n factorial minus the number of repeated items

• n factorial plus the number of repeated items

• n factorial multiplied by the number of repeated items

• n factorial divided by the product of factorials of repeated items

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CCSS.7.EE.A.2

CCSS.HSA.SSE.A.2

In the example, how many letters are there in total?

• Ten

• Seven

• Eight

• Nine

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CCSS.L.1.2D

CCSS.RF.2.3E

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How many A's are there in the example?

• One

• Two

• Four

• Three

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CCSS.L.1.2D

CCSS.L.K.2C

CCSS.RF.2.3E

CCSS.RF.4.3A

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How many B's are there in the example?

• Three

• One

• Four

• Two

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CCSS.7.EE.A.1

How many D's are there in the example?

• Two

• Four

• Three

• One

What is the first step in simplifying the permutation calculation?

• Multiply all numbers

• Add all numbers

• Subtract all numbers

• Expand nine factorial

What is the result of simplifying nine factorial divided by three factorial?

• One

• Two

• Three

• Four

What is the final result of the permutation calculation?

• Seven thousand sixty

• Six thousand fifty

• Four thousand thirty

• Five thousand forty

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CCSS.RI.11-12.4

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What is the purpose of using a calculator in the final section?

• To change the formula

• To verify the manual calculation

• To start a new calculation

• To find the number of letters

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CCSS.RI.11-12.4

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CCSS.RI.9-10.4