📘 combinatorics

1. **Problem 14:** Jan grabs a pair of slippers from 4 people (Joe, Jan, Jen, Jun), each with a pair of slippers. We want the probability that Jan did *not* grab a matching pair. 2

1. **பிரச்சினை விளக்கம்:** 5 தூப்பாட்ட மடைகள், 4 நந்துகள் மற்றும் 3 கையுறைகள் 6 மாணவர்களுக்கு பகிரப்படுகின்றன.

1. **State the problem:** Evaluate the combination expression $11 C 2$. 2. **Formula:** The combination formula is given by

1. The problem asks to evaluate the combination $14C5$, which represents the number of ways to choose 5 items from 14 without regard to order. 2. The formula for combinations is:

1. The problem asks to evaluate the combination expression $15C4$, which represents the number of ways to choose 4 items from 15 without regard to order. 2. The formula for combina

1. **Problem statement:** (a) Find how many 3-digit and 4-digit numbers can be formed using digits 4, 5, 6, 7, 8 without repetition.

1. The problem is to evaluate the binomial coefficient $\binom{2}{2}$. 2. The binomial coefficient $\binom{n}{k}$ is defined as:

1. **Problem Statement:** (A) How many ways can a 4-person subcommittee be selected from a committee of 8 people?

1. **State the problem:** We want to find how many different possible finishes there are for the first 3 places in a horse race with 18 horses, excluding ties. 2. **Formula used:**

1. The problem asks to evaluate the combination $7 C 3$, which represents the number of ways to choose 3 items from 7 without regard to order. 2. The formula for combinations is:

1. **Problem statement:** Find the number of license plates with 4 letters followed by 2 digits where no letters or digits are repeated. 2. **Formula and rules:**

1. **Problem statement:** We want to find the number of different license plates possible with 4 letters followed by 2 digits. 2. **Total possible license plates:** Each of the 4 l

1. **Stating the problem:** We need to find the number of different 5-digit combinations possible on a lock with 5 wheels labeled 0 to 9 when successive digits must be different. 2

1. **Stating the problem:** We need to find the number of different 5-digit combinations possible on a lock with 5 wheels labeled 0 to 9 when digits can be repeated. 2. **Understan

1. **Stating the problem:** We need to find the number of different 5-digit combinations possible on a lock with 5 wheels labeled 0 to 9 under different conditions. 2. **Understand

1. **Problem Statement:** We need to find how many 2-character passwords are possible using the English alphabet with case sensitivity. 2. **Understanding the problem:** The Englis

1. **Problem statement:** How many 2-letter code words can be formed from the letters X, N, I, M, A, P under three conditions: - No letter is repeated.

1. **Problem:** How many different combinations of six numbers can be chosen from the digits 1 to 8 if each digit is chosen only once? 2. **Formula:** The number of combinations of

1. **State the problem:** Maeve’s team plays 5 matches, and we want to find the total number of different possible outcomes for these matches. 2. **Understand the outcomes:** Each

1. **Stating the problem:** We have 5 class prefects: Eimear (E), Samantha (S), Mia (M) who are girls, and Paul (P), Neil (N) who are boys. We need to find all possible pairs of on

1. **Problem statement:** (a)(i) A restaurant offers a three-course meal with 4 starters, 6 main courses, and 8 desserts. We need to find the total number of different three-course