Q How many possible sets of 7 marbles are there? | |||||||
A The number of possible sets of 7 marbles is called C(10, 7). Other notations for it are | 10C7 | and |
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Computing C(10, 7) by hand
1. Create a faction with 10 in the numerator and 7 in the denominator: |
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2. Extend the term in the denominator to its factorial: |
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3. Extend the term in the denominator to as many terms as in the denominator: |
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4. Compute it (it helps to first cancel the terms in the denominator): |
| = | 120 |
C(5, 2) = |
| = | 10 | C(5, 5) = |
| = | 1 |
Some Special Cases:
Computation Utility:
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