# Question #51bb7

Jun 16, 2017

See explanation.

#### Explanation:

The question is not clearly stated, but I will try to answer it.

The problem is: "Can a pizza have more than one identical topping?"

• If there can be more than one identical topping, then the number of ways can be calculated as:

$n = 4 \times {10}^{3} = 4 , 000$

The number comes from multiplying number of cheese types, and the number of toppings (3 times)

• if the toppings cannot be different, then the number is:

$n = 4 \times 10 \times 9 \times 8 = 2 , 880$

The number is calculated as follows:

• cheese can be chosen in 4 ways,

• the first topping can be chosen in 10 ways

• the second topping can be chosen in 9 ways (it cannot be the same as the first one)

• the third topping can be chosen in 8 ways (it cannot be the same as the first and the second one)

Hope that helps.