example 4 use pascal’s triangle school clubs the 6 members of a model un club must choose 2...

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EXAMPLE 4 Use Pascal’s triangle School Clubs The 6 members of a Model UN club must choose 2 representatives to attend a state convention. Use Pascal’s triangle to find the number of combinations of 2 members that can be chosen as representatives. SOLUTION Because you need to find 6 C 2 , write the 6th row of Pascal’s triangle by adding numbers from the previous row.

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Page 1: EXAMPLE 4 Use Pascal’s triangle School Clubs The 6 members of a Model UN club must choose 2 representatives to attend a state convention. Use Pascal’s

EXAMPLE 4 Use Pascal’s triangle

School Clubs

The 6 members of a Model UN club must choose 2 representatives to attend a state convention. Use Pascal’s triangle to find the number of combinations of 2 members that can be chosen as representatives.

SOLUTION

Because you need to find 6C2, write the 6th row of Pascal’s triangle by adding numbers from the previous row.

Page 2: EXAMPLE 4 Use Pascal’s triangle School Clubs The 6 members of a Model UN club must choose 2 representatives to attend a state convention. Use Pascal’s

EXAMPLE 4 Use Pascal’s triangle

n = 5 (5th row) 1 5 10 10 5 1

n = 6 (6th row) 1 6 15 20 15 6 1

6C0 6C1 6C2 6C3 6C4 6C5 6C6

ANSWER

The value of 6C2 is the third number in the 6th row of Pascal’s triangle, as shown above. Therefore, 6C2 = 15. There are 15 combinations of representatives for the convention.

Page 3: EXAMPLE 4 Use Pascal’s triangle School Clubs The 6 members of a Model UN club must choose 2 representatives to attend a state convention. Use Pascal’s

GUIDED PRACTICE for Example 4

WHAT IF? In Example 4, use Pascal’s triangle to find the number of combinations of 2 members that can be chosen if the Model UN club has 7 members.

6.

ANSWER 21 combinations

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