In choosing what music to play at a charity fund raising event, Shaun needs to have an equal number of string quartets from Mendelssohn, Beethoven, and Haydn. If he is setting up a schedule of the 66 string quartets to be played, and he has 66 Mendelssohn, 1616 Beethoven, and 6868 Haydn string quartets from which to choose, how many different schedules are possible? Express your answer in scientific notation rounding to the hundredths place.

64.69e221

Step-by-step explanation:

When choosing, the combination formula for selection is used. That is when selecting "r" number of items from a possible "n" items, then the number of ways is denoted as:

nCr = n! / (n-r) ! * r!

Since 66 string quartet have to be chosen and the 3 genres must be equally represented in the string quartet, then we must have 22 number of each genre in it.

Number of ways to select 22 mendelssohn from possible 66 = 66C22 = 1.82 * 10^17

Number of ways to select 22 Beethoven from possible 1616 = 1616C22 = 2.97 * 10^49

Number of ways to select 22 Haydn from possible 6868 = 6868C22 = 2.2 * 10^63

Total number of ways to arrange these 66 schedules = 66! = 5.44 * 10^92

Number of possible schedule = [1.82 * 10^17] * [2.97*10^49] * [2.2*10^63] * [5.44*10^92]

=64.69 * 10^221. ≈64.69e221