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Permutations and Combinations

The document presents a series of problems related to permutations and combinations, asking for the number of distinguishable arrangements of letters and various scenarios involving selections and arrangements of objects. It includes examples with letters, flags, shirts, people, and other items, requiring calculations based on the principles of combinatorics. The problems range from simple arrangements to more complex selections from larger groups.

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13 views4 pages

Permutations and Combinations

The document presents a series of problems related to permutations and combinations, asking for the number of distinguishable arrangements of letters and various scenarios involving selections and arrangements of objects. It includes examples with letters, flags, shirts, people, and other items, requiring calculations based on the principles of combinatorics. The problems range from simple arrangements to more complex selections from larger groups.

Uploaded by

al26061
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Permutations and Combinations

For examples #1 – 8, find the number of distinguishable permutations you can make using
the letters of each:
1) MATH 2) ALGEBRA

3) FIREBIRD 4) COMMITTEE

5) CINCINNATI 6) MISSISSIPPI

7) MILLIONAIRE 8) SUBSTITUTE
9) How many vertical arrangements are there of 9 flags if 5 are blue, 3 are green, and 1 is
orange?

10) How many ways can you stack 10 shirts if 6 are pink, 2 are purple, and 2 are yellow?

11) How many ways can 6 people stand in a line?

12) In how many ways can 8 runners come in first, second, and third place?

13) Your English teacher asked you to read 2 novels from a choice of 12 novels. In how many
ways can you choose which books to read?
14) How many ways are there to select 3 rings from a box of 15?

15) In how many different ways can 5 of 9 kinds of bushes be planted in front of the school?

16) A class has 105 students. In how many ways can they choose a president, vice-president,
and secretary if only one person can hold each position?

17) In how many ways can a committee of 4 people be chosen from a pool of 30 employees?

18) If 18 students enter an art contest, how many ways can 5 honorable mention certificates be
awarded?
19) How many different combinations of 6 numbers are there from a lottery ticket of 54
numbers?

20) Tim has to visit 5 family members. In how many different ways can he visit them?

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