If 5 integers are to be selected at random and without replacement from the list consisting of the 20 integers from 1 to 20, inclusive, what is the probability that 2 of the 5 selected integers will be 10 and 20 ? A. 2/5 B. 1/4 C. 1/10 D. 1/19 E. 1/60 OK, I’ll be … Read More
If a club has 12 members, what is the ratio of the number of different possible 6-member committees that can be formed to the number of different possible 5-member committees that can be formed? Congratulations! If you have memorized the Combination formula and desperately want to use it but are beginning to realize that (naturally) … Read More
A certain identification code consists of 6 digits, each of which is chosen from 1, 2, …, 9. …The same digit can appear more than once. If the sum of the 1st and 3rd digits is the 5th digit, and the sum of the 2nd and 4th digits is the 6th digit, how many identification … Read More
GMAT Combinatorics: The Ultimate Guide to GMAT Factorials — the Three-Question Method If we don’t get the concept of Factorials straight, the rest of this–Permutations and Combinations, quite a lot of advanced GMAT fatoring, etc.–is never going to work. How to Think About GMAT Factorials in a Broad Sense The idea of a Factorial is … Read More
GMAT Combinatorics Questions: Permutations vs. Combinations (plus Shorthand!) As noted above, this is simply a clipped factorial. Let’s take the case from above and modify it slightly. Three paintings, from a group of seven total paintings, are chosen to be hung on a wall. In how many ways can these three paintings be arranged? So: … Read More
GMAT Combinatorics: an Introduction Ever wonder why GMAT Permutations and Combinations seem to hard to learn? There’s no good reason–that’s just because they tend to be explained in a terrible way. It’s time for us to fix that! At the risk of blowing all the secrets too early, let’s do this at the beginning. If … Read More