Can you explain this on paper for a better understanding?

Combinations I. In how many ways can 12 prizes be awarded evenly among four people? 2.From a deck of 52 cards, how many different four-card hands could be dealt which include one card from each suit? 3.From 6 people, how many ways can a committee of at least one member be chosen? Chapter 3: The Binomial Theorem 1.Find the binomial expansion the expansion of ( 1+ y )* 7 2. ( 2x+ 1 )6. 3.( x- 2y )48 4. Write the third term in the expansion of ( I+ y ) 6 5. Write the fifth term in the expansion of ( x + 2y )6 Chapter 6 (New Text): Introduction to Probability 1. Two dice are rolled. What is the probability that the sum of the rolls is less than 4? 2. What is the probability that there are at least two people with the same birthday in a class of 40 students? Answer: 0.891 3. Determine the number of elements in the Sample Space for each of the following: K/U3 COMM2 Tossing a coin three times Rolling a dice Tossing a pair of dice. 4. Determine the theoretical probability of K/U 5 Getting sum 4 with 2 dice Getting sum at least 6 with 2 Dice Getting an even number on both dice Getting sum equal to even number Getting an even and an odd number