Consider the expansion (x + 2)^11 what are the number of terms in this expansion. find the term containing x^2

You have the three components for each term:-The x component, which will have power n-k.-The y component (or in this question, y=2 so we will have a power of 2), so for term k we will have 2^k.-The binomial coefficient.
Since we know the value of y the numbers in the expansion will come from the binomial coefficient multiplied by the respective power of 2. Let me give another example:Say we want the term with x^7. Then n-k=7, so 11-k=7 and k=4.
So for the numbers which multiply x^7, we will have:2^k=2^4=16.The binomial coefficient 11C4=330.Multiplying these together we get the term 5,280x^7.

The answer would be 27 because assuming that each package has 1 bar of soap and 1 tube of toothpaste, after 27 packages they would run out of toothpaste