Combinations Worksheet

                    Lesson 1

Problem:    There are 10 boys and 18 girls in class.  Find the number of combinations of teams of 6 students that can be selected from the class to work on a group project.  A team consists of 4 students.                                                                                               

Solution     To find all of the different ways to arrange r items out of n items.

Step 1:       Use the combination formula below.

n stands for the total number of items;

r stands for how many things you are choosing.

Solution      ⁿCk = n! for 0≤r≤n

Step 2: r! (n-r)! .

Solution      Total number of students in class = 10 Boys + 18 girls

Step 3: = 28 students

Solution      ⁿCk = 28! = 28! = 682 ways

Step 4: 6! (28-4)! 6x5x4x3x2x1(24!)

Solution Answer is : 682 ways

Try two practice problems:  

Find the combinations in selecting the following.

(A) Letters NI in the word MANIFEST.

(B) Combination of two letters in NASA.

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