Answer:
1. [tex]\dfrac{1}{16}[/tex]
2. 30
Step-by-step explanation:
1. The probability of drawing a spade from a standard 52-card deck is
[tex]\dfrac{13}{52}=\dfrac{1}{4}.[/tex]
After replacing it, and then drawing another card, the probability of drawing another spade is also [tex]\dfrac{1}{4}.[/tex]
Thus, the probability of drawing a spade from a standard 52-card deck, replacing it, and then drawing another spade is
[tex]\dfrac{1}{4}\cdot \dfrac{1}{4}=\dfrac{1}{16}.[/tex]
2. The word FABRIC consists of 6 different letters. The number of permutations that can be formed using 2 letters at a time is
[tex]P_6^2=\dfrac{6!}{(6-2)!}=\dfrac{6!}{4!}=\dfrac{4!\cdot 5\cdot 6}{4!}=5\cdot 6=30.[/tex]
