Answer:
[tex]\dfrac{400}{1,001}\approx 0.3996[/tex]
Step-by-step explanation:
There are 10 unique consonant tiles an 5 unique vowel tiles, 15 tiles in total.
You can select 5 different tiles in
[tex]C^{15}_5=\dfrac{15!}{5!(15-5)!}=\dfrac{11\cdot 12\cdot 13\cdot 14\cdot 15}{2\cdot 3\cdot 4\cdot 5}=11\cdot 13\cdot 7\cdot 3=3,003[/tex]
different ways.
You can select 3 different consonants and 2 different vowels in
[tex]C^{10}_3\cdot C^5_2=\dfrac{10!}{3!(10-3)!}\cdot \dfrac{5!}{2!(5-2)!}=\dfrac{8\cdot 9\cdot 10}{2\cdot 3}\cdot \dfrac{4\cdot 5}{2}=4\cdot 3\cdot 10\cdot 2\cdot 5=1,200[/tex]
different ways.
Thus, the probability is
[tex]Pr=\dfrac{1,200}{3,003}=\dfrac{400}{1,001}\approx 0.3996.[/tex]
