An order comes in for 5 palettes of low grade shingles. In the warehouse there are 10 palettes of high grade, 15 of medium grade, and 20 of low grade shingles. An inexperienced shipping clerk is unaware of the distinction in grades of asphalt shingles and he ships 5 randomly selected palettes. 1 How many different groups of 5 palettes are possible?

1,221,759 groups

Step-by-step explanation:

Total number of palettes = 10 + 15 + 20 = 45 palettes

Number of palettes chosen = 5 palettes

C (n, r) = n! / r! (n-r) !

Where,

C, is the number of possible combinations

n, is the total number of palettes in the set

r, is the number of palettes chosen from the set

n = 45 palettes

r = 5 palettes

Therefore,

C = 45! / 5! (45 - 5) !

C = 45! / 5! (40) !

C = 45*44*43*42*41 / 5*4*3*2*1

C = 146611080/120

C = 1,221,759

Therefore there are 1,221,759 possible combinations of 5 palettes from the 45 palettes available.