Question

1. A standard deck of playing cards has 52 cards: 13 spades, 13 clubs, 13 hearts, and 13 diamonds. What is the probability of drawing a spade from a standard 52-card deck, replacing it, and then drawing another spade? Show your work or explain how you got your answer.
2. Using the letters in the word FABRIC, find the number of permutations that can be formed using 2 letters at a time. Show your work or explain how you got your answer.

Answer 1

Answer:

1. $\dfrac{1}{16}$

2. 30

Step-by-step explanation:

1. The probability of drawing a spade from a standard 52-card deck is

$\dfrac{13}{52}=\dfrac{1}{4}.$

After replacing it, and then drawing another card, the probability of drawing another spade is also $\dfrac{1}{4}.$

Thus, the probability of drawing a spade from a standard 52-card deck, replacing it, and then drawing another spade is

$\dfrac{1}{4}\cdot \dfrac{1}{4}=\dfrac{1}{16}.$

2. The word FABRIC consists of 6 different letters. The number of permutations that can be formed using 2 letters at a time is

$P_6^2=\dfrac{6!}{(6-2)!}=\dfrac{6!}{4!}=\dfrac{4!\cdot 5\cdot 6}{4!}=5\cdot 6=30.$