In algebra, 9C3 Times 26P3 combines a combination and a permutation, and it often appears in counting problems where you need to first pick a group and then arrange a subset. Understanding how to compute 9C3 Times 26P3 helps you solve many practical problems with confidence.
What do the notations mean?
9C3 represents a combination: the number of ways to choose 3 items from 9 when order does not matter. It equals 9!/(3!6!) = 84. 26P3 represents a permutation: the number of ordered ways to select 3 items from 26. It equals 26×25×24 = 15600.
Step-by-step calculation
Compute each piece separately and then multiply. Here are the exact steps:
9C3 = 9!/(3!6!) = 84
26P3 = 26!/(26−3)! = 26×25×24 = 15600
Finally, multiply the two results: 84 × 15600 = 1,310,400.
Key Points
- Combining a choose and a permutation is a common pattern in counting problems, and it requires treating each component distinctly.
- 9C3 equals 84, which comes from 9!/(3!6!).
- 26P3 equals 26×25×24, because permutations count ordered selections.
- Multiplying the two results gives the total number of ways for the combined process, here 1,310,400.
- Double-check arithmetic by breaking the calculation into easy steps and verifying each part separately.
What does 9C3 mean in combinatorics?
+9C3 is the number of ways to choose 3 items from 9 when order does not matter. It equals 84. The formula is 9!/(3!6!).
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<h3>How is 26P3 calculated, and what does it count?</h3>
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<p>26P3 counts the number of ordered samples of 3 items drawn from 26. It is computed as 26×25×24 = 15600.</p>
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<h3>Why multiply a combination by a permutation in problems like 9C3 Times 26P3?</h3>
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<p>Because you first pick a group of 3 from 9 without regard to order, then choose and arrange 3 items from 26. The total count is the product 84 × 15600.</p>
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<h3>Is 9C3 Times 26P3 always equal to 1,310,400?</h3>
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<p>Not always, but for this specific calculation it is: 9C3 = 84 and 26P3 = 15600, and 84×15600 = 1,310,400.</p>
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