11 grade maths others
How do you evaluate {}^8{C_2}?
How do you evaluate {}^8{C_2}?
1 Answer
Askiitians Tutor Team
To evaluate the expression {}^8C_2, which represents the combination of selecting 2 items from a set of 8 items, you can use the formula for combinations:
{}^nC_r = n! / (r! * (n - r)!)
In this case, we have:
{}^8C_2 = 8! / (2! * (8 - 2)!)
Let's calculate it step by step:
Calculate the factorial of 8: 8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40320.
Calculate the factorial of 2: 2! = 2 * 1 = 2.
Calculate the factorial of (8 - 2) = 6: 6! = 6 * 5 * 4 * 3 * 2 * 1 = 720.
Plug in the values into the combination formula:
{}^8C_2 = 40320 / (2 * 720) = 40320 / 1440 = 28.
Therefore, the value of {}^8C_2 is 28.
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