Answer: 8 * 7 = 56 different ways!
The correct answer is B.
The correct answer is B.
A girl has to make pizza with different toppings. There are 8 different toppings. In how many ways can she make pizzas with 2 different toppings? A) 16 b) 56 c) 112 d) 28
The answer is 8 * 7 because the formula is n!/(n-c)! Where n is the total number of things and C is the number chosen in a grouping. In this problem n=8 and c=2 so we get 8!/(8-2)! = (8*7*6*5*4*3*2*1)/(6*5*4*3*2*1) = 8*7=56
Don't cheat on your homework its the wrong way to go
To see why this is so you may want to get a bit practical with it! Do a 'cross table' with all the 8 pizza toppings arranged as below:
1 2 3 4 5 6 7 8
1 (1,1) (1,2) (1,3) ......
2 (2,1)
3 (3,1) .
.
From the complete table, you can count the number of distinct pairings of two different toppings as read from the entries. Clearly, this is not an efficient method for bigger numbers and a formula can be learnt and be applied as appropriate. I note that you have been assisted on this front.
1 2 3 4 5 6 7 8
1 (1,1) (1,2) (1,3) ......
2 (2,1)
3 (3,1) .
.
From the complete table, you can count the number of distinct pairings of two different toppings as read from the entries. Clearly, this is not an efficient method for bigger numbers and a formula can be learnt and be applied as appropriate. I note that you have been assisted on this front.