Find the sum of the numbers in each row, except row 0, of the portion of Pascal’s triangle shown above. What       pattern do you observe concerning these sums? Predict the sum of the numbers in row 9 of Pascal’s triangle

How many different passwords are there that contain only digits and lower-case letters, subject to the restrictions that the password must be 6 characters long and contain at least one digit. Your answer can be a single number or a formula with numbers filled in.

Pascals Triangle  Example and Non-Example

How many numbers have digits which are all ”1”s and ”2”s, and thedigits add up to 8? A few such numbers are 12212, 112121, and 112121. (HINT: breakthe list into cases and count each one. You can count them by hand, but you will savea lot of time if you apply the right formula.)

12) Use Pascals Triangle to exp and the binomial powers. (x- 3)^3=

In how many ways can the word "MATHAMATICS" be arranged if no two M's are next to one another?

10. Write the first five rows of s triangle. the ĕxpansion (x-y)" Pascal's Write