How many possibilities are there for the Winner, 1st runner-up, and 2nd runner-up places in a singing competition with 11contestants if all orders of single ranking are possible?a. 992.00b. 989.00c. 990.00d. 991.00e. None of the Options are correct

The number of possibilities can be calculated using the formula for permutations, which is nPr = n! / (n - r)!. In this case, n is the total number of contestants (11) and r is the number of positions to fill (3: Winner, 1st runner-up, and 2nd runner-up).

Step 1: Calculate n! (factorial of n) 11! = 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 39,916,800

Step 2: Calculate (n - r)! (n - r)! = (11 - 3)! = 8! 8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320

Step 3: Divide n! by (n - r)! nPr = n! / (n - r)! = 39,916,800 / 40,320 = 990

So, there are 990 different ways to arrange the 11 contestants in the top 3 positions. Therefore, the correct answer is c. 990.00.