What is 5 choose 2?
Understand the Problem
The question is asking for the mathematical computation of '5 choose 2', which refers to the number of ways to choose 2 elements from a set of 5 distinct elements. This can be calculated using the formula for combinations.
Answer
The number of ways to choose 2 elements from 5 is \( 10 \).
Answer for screen readers
The answer is ( 10 ).
Steps to Solve
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Recall the Combination Formula
The formula for combinations is given by:
$$ C(n, r) = \frac{n!}{r!(n - r)!} $$
where ( n ) is the total number of elements, ( r ) is the number of elements to choose, and ( ! ) denotes factorial. -
Identify the Values
For the problem "5 choose 2":
- ( n = 5 ) (total elements)
- ( r = 2 ) (elements to choose)
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Substitute the Values into the Formula
Substituting ( n ) and ( r ) into the combination formula:
$$ C(5, 2) = \frac{5!}{2!(5 - 2)!} $$ -
Calculate the Factorials
Calculating the factorials:
- ( 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 )
- ( 2! = 2 \times 1 = 2 )
- ( (5 - 2)! = 3! = 3 \times 2 \times 1 = 6 )
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Plug the Factorials Back into the Formula
Now substituting the calculated factorials:
$$ C(5, 2) = \frac{120}{2 \times 6} $$ -
Perform the Final Calculation
Calculating ( C(5, 2) ):
$$ C(5, 2) = \frac{120}{12} = 10 $$
The answer is ( 10 ).
More Information
The result indicates that there are 10 different ways to choose 2 elements from a set of 5 distinct elements. This type of calculation is widely used in statistics and probability to determine possible outcomes.
Tips
A common mistake is miscalculating factorial values, especially when handling larger numbers. Always double-check your factorial calculations to ensure accuracy.
