# Thread: Jalapeņos and Eggs... how many combinations for this set of numbers. THANK YOU

1. ## Jalapeņos and Eggs... how many combinations for this set of numbers. THANK YOU

I used to know how to get the answer... but forgot. Welcome any help on this.

PROBLEM:
There are no more that 56 eggs and no less than 27.
There are no more than 13 jalapenos and no less than 2.

NEED TO FIND:
How many combinations can there be given this set of numbers,
and how can it be found.

Brian

2. Hello, Brian!

You're right, awkward . . . I overlooked the "no less than" . . . *blush*

There are no more that 56 eggs and no less than 27.
There are no more than 13 jalapenos and no less than 2.

How many combinations can there be given this set of numbers?

We have: . $\displaystyle \begin{array}{ccccc}27 &\le& \text{eggs} &\le& 56 \\ \\[-4mm] 2 &\le& \text{jalapenos} &\le & 13 \end{array}$

$\displaystyle \begin{array}{cccccccc}\text{Choices for eggs:} & \underbrace{27,28,29,\hdots 56}_{\text{30 choices}} \\ \\[-2mm] \text{Choices for jalapenos:} & \underbrace{2,3,4, \hdots 13 }_{\text{12 choices}} \end{array}$

Number of combinations: . $\displaystyle 30\!\cdot\!12 \:=\:360$

3. Thanks for the help

SOLVED

4. ?
Soroban, I don't see how zero is a possible choice for the number of eggs when we are told that there are "no less than 27".

(Just a minor nit-pick.)