# How many customers didn't put any toppings, and how many had ketchup?A hamburger seller offers its customers Ketchup, Mustard, and Relish as toppings. The following table shows the toppings...

How many customers didn't put any toppings, and how many had ketchup?

A hamburger seller offers its customers Ketchup, Mustard, and Relish as toppings. The following table shows the toppings selected by the 1600 customers who bought hamburgers from them. (All inclusive)

Topping / Number Of Customers

Ketchup 944

Mustard 771

Relish 656

Ketchup & Mustard 551

Ketchup & Relish 318

Mustard & Relish 186

All Three 186

a) How many customers didn't put any toppings?

b) How many put ketchup?

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We can do this using set theory and set calculations. I will use the following notations.

Ketchup - K

Mustard - M

Relsih - R

Therefore according to given data.

`S = 1600`

`K = 944`

`M = 771`

`R = 656`

`K nn M = 551`

`K nn R = 318`

`M nn R = 186`

`K nn M nn R = 186`

Let's find first how many customers did put toppings.

That is,

`K uu M uu R`

According to set rules,

`K uu M uu R = K + M + R -(K nn M) - (K nn R) - (M nn R) + (K nn M nn R)`

Therefore,

`K uu M uu R =944+771+656-551-318-186+186`

`K uu M uu R = 1502`

Therefore, the number of customers who had one or more toppings is 1502.

**Therefore number customers who didn't get toppings **

** = 1600-1502**

** = 98**

The number of customers who put only ketchup = K1

`K1 = K -(K nn M) - (K nn R) + (K nn M nn R)`

`K1 = 944 -551-318+186`

`K1 = 261`

**Therefore, the number of customers who got only ketchup is 261.**