In the diagram below, the radius of each of the smaller circles is r. What is the radius of the larger circle?
Year: 2024
Solution to Toy Box – Fall 2023
Problem: If all possible (distinguishably different) arrangements of the letters A, C, C, L, L, S, U, and U are put in alphabetical order, in what position is the word “CALCULUS”?
Solution: The total number of distinguishably different arrangements of the letters A, C, C, L, L, S, U, and U is given by
To find the appearance of “CALCULUS,” we first, we need to “clear” all the arrangements that begin with A, of which there are
Those arrangements that begin with “CAC” will appear next on the list and need to be cleared as well. There are
of these, the number of distinguishable arrangements of the remaining letters L, L, S, U, and U.
The next several entries on the list will begin with “CALC,” followed by the letters L, S, U, and U. We can first clear the arrangements that start with “CALCL,” numbering
and then those that begin “CALCS,” which also number
Then the next arrangement on the list is “CALCULSU,” followed immediately by “CALCULUS.” Hence, “CALCULUS” appears in position number
630 + 30 + 3 + 3 + 1 + 1 = 668.
MAT Community Tea & Coffee Hour on F 2/2
Throughout the year, the Math Department hosts a number of informal events meant to help build and sustain our mathematical sciences community here at DePaul. These events provide an opportunity to meet with fellow MAT students, at both undergraduate and graduate levels, as well as MAT faculty members in a relaxed setting.
Our next event will take place on Friday, 2/2 at 10:30-11:45 am in the MAT Department office suite (on the 5th floor of SAC). Light refreshments, such as coffee, tea, and cookies, will be served. We hope that you can join us.
MAT Community Tea & Coffee Hour on 1/19
Throughout the year, the Math Department hosts a number of informal events meant to help build and sustain our mathematical sciences community here at DePaul. These events provide an opportunity to meet with fellow MAT students, at both undergraduate and graduate levels, as well as MAT faculty members in a relaxed setting.
Our next event will take place this Friday, 1/19 at 1:30-2:45 pm in the MAT Department office suite (on the 5th floor of SAC). Light refreshments, such as coffee, tea, and cookies, will be served. We hope that you can join us.