given a standard 52 card deck, how many possible hands have 2 face cards and 1 distinct, order doesn't matter (I am looking for the possible hands, not possible ways to draw those hands.)

Suppose you visit a small, local panadería and decide to pick up some pasteries. The panadería has a selection of 8 different cupcakes, 14 different donuts ,7 different muffins ,2 types of donut holes , and 11 different types of pan dulce. You  pick one of each. How many different orders are possible.

You and two friends decide to go to a casino and play Blackjack. You find an empty table and sit down. The dealer shuffles and deals from a new 52 card deck. In order to win, you and your friends know that you need to either score a 21 (blackjack and automatic win) or get a higher total than the dealer. You know that a deck of cards has 13 different cards (2-10, Jack, Queen, King, and Ace), and that there are 4 copies of each in the deck. You know that an ace is equal to either 1 or 11 and that Jacks, Queens, and Kings are worth 10. The dealer deals out the following cards: You: Jack and Ace Friend 1: King and 10 Friend 2: 10 and 10 Dealer: 10 and ? The dealer is about to deal their last card. What are the following probabilities: A) What is the probability that the next card can beat your hand?   B) What is the probability that the next card can tie your hand?   C) What is the probability that the next card can beat your friends?

Your club would like to form a committee that has 2 sophomores, 3 juniors, and 4 seniors. If there are 7 sophomores, 8 juniors, and 6 seniors in the club, how many different ways can the committee be formed? Assume that the order that you are picked in does not matter.

A jar of jellybeans has three different colors of jellybeans:  green,  red, and yellow. Let’s use symbols to represent each color: green = g, red = r, and yellow = y. If you choose a handful of four jellybeans from the jar, how many different combinations of jellybeans are possible? Assume there are at least four of each color.

In the local boating pond there are 10 plain wooden boats, each with a different number. The owner decides that some of these boats will be painted: one in blue, one in green, one in red, and one in orange, and the remaining ones left unpainted. How many ways are there to paint the boats? The number of ways is

Suppose Fred has 2 pairs of pants (blue and black) and 3 shirts (red, blue, and black).  Which of the following represents all of the outfits Fred could make with these options?

A standard deck of cards contains a total of 52 cards: There are four suits (hearts, diamonds, clubs, and spades), each of which have 13 face values (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King). Suppose 6 cards are drawn, without replacement. How many of these 6 card hands will contain exactly 1 spades?

Solve the problem. Describe all solutions of Ax = b, where 2-5 31 A = -2 6-5 70 and b = 310 Describe the general solution in parametric vector form. -3 G -8-17-0

Suppose we want to choose   3 colors, without replacement, from the   4 colors red, blue, green, and purple.       How many ways can this be done, if the order of the choices does not matter?   How many ways can this be done, if the order of the choices does matter?