find the value of 5c3
What is the value of 5c3?
Answer:
The value of 5c3, denoted as “5 choose 3,” represents the number of ways to choose 3 items from a set of 5 distinct items, without considering the order of selection. The formula to calculate this is given by the binomial coefficient formula:
[ \binom{n}{r} = \frac{n!}{r! \times (n-r)!} ]
Using this formula, the value of 5c3 can be calculated as:
[ \binom{5}{3} = \frac{5!}{3! \times (5-3)!} = \frac{5 \times 4 \times 3 \times 2 \times 1}{(3 \times 2 \times 1) \times (2 \times 1)} = 10 ]
Therefore, the value of 5c3 is 10. This means there are 10 different combinations of choosing 3 items from a set of 5 items.