Too Many Options

Probability Level 3

There is a sandwich shop in my area that sells various types of bread and ingredients. The number of the variety of bread and the number of the variety of ingredients to choose differ by one.

I am told that if I want exactly one specific bread and one specific ingredient, then the total possible choices that I have is in between 40 and 50.

What is the sum of the total number of the variety of bread and the total number of the variety of ingredients to choose from?

The answer is 13.

2 solutions

Achal Jain
Jun 18, 2016

First we are told that the number of bread and ingredients differ by one. So let number of bread be $n$ and number of ingredients be $n+1$ . So now total ways to choose one from each is-

$_{ 1 }^{ n }{ C }\times _{ 1 }^{ n+1 }{ C }$ . This lies between 40 and 50.

After opening it we get the result $n(n+1)$ . Only possible value of n=6. Therefor answer comes out to be $6+7=13$

Pedro Thomasi
Jun 19, 2016

6x5 = 30 low -6x7 = 42 fine -7x8 = 56 higher

6 and 7. 13

Too Many Options

The answer is 13.

2 solutions

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