The word geometry has eight letters. three letters are chosen at random. what is the probability that two consonants and one vowel are chosen? 0.536 0.268 0.179 0.089

Answer:0.536 is the required probability.Step-by-step explanation:  We have been given the word the word "GEOMETRY" we have to find the probability that two consonants and one vowel are chosen:Number of consonants are: 5Number of  vowels are: 3Hence, The required probability is: [tex]\frac{^5C_2\cdot ^3C_1}{^8C_3}[/tex]Using: [tex]^nC_r=\frac{n!}{(r!)(n-r)!}[/tex][tex]\frac{\frac{5!}{3!\cdot 2!}\cdot\frac{3!}{1!\cdot 2!}}{\frac{8!}{3!\cdot 5!}}[/tex]Simplifying the above expression:[tex]\frac{\frac{5\cdot 4\cdot 3!}{3!\cdot 2}\cdot {\frac{3\cdot 2!}{2!}}}{\frac{8\cdot 7\cdot 6\cdot 5!}{5!\cdot 3\cdot 2}}[/tex]Further simplification after cancelling out the common terms we get:[tex]\Rightarrow \frac{30}{56}=\frac{15}{28}=0.5357=0.536[/tex]Hence, Option 1 is correct.