There are 10 contestants in a scrabble tournament. The number of ways in
which the 3 finalists can be chosen is closest to?
To find the number of ways in which the 3 finalists can be chosen among 10 contestants, we can use the combination formula. The combination formula is given by:
C(n, r) = n! / (r!(n-r)!),
where n is the total number of contestants and r is the number of finalists to be chosen.
In this case, we need to find C(10, 3).
Plugging the values into the formula, we get:
C(10, 3) = 10! / (3!(10-3)!)
= 10! / (3!*7!)
Now, we can calculate the factorial values:
10! = 10 * 9 * 8 * 7! = 10 * 9 * 8 * 7 * 6!
3! = 3 * 2 * 1 = 6
7! = 7 * 6!
Now, substituting the values:
C(10, 3) = (10 * 9 * 8 * 7 * 6!) / (6! * 7!)
The factorial terms in the numerator and denominator cancel out:
C(10, 3) = (10 * 9 * 8) / (3 * 2 * 1)
= 720 / 6
= 120
Therefore, the number of ways in which the 3 finalists can be chosen from 10 contestants is 120.