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Higgins was asked to make a unique three-letter arrangement using only letters from the word home. He can use each letter only once. (His arrangement doesn’t need to be a valid word.)

:The probability that Higgins forms a three-letter arrangement with vowels as the second and third letters is
1/3 1/4 1/6 1/8

The probability that Higgins forms a three-letter arrangement with two consecutive consonants is
1/3 1/4 1/6 1/8

User Hoa Vu
by
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2 Answers

6 votes

Answer:

Answer: 1) Third option is correct.

2) First Option is correct.

Explanation:

User Osotorrio
by
8.6k points
2 votes

Answer: 1) Third option is correct.

2) First Option is correct.

Explanation:

Since we have given that

There is unique three- letter arrangement using only letters from the word home.

so, The total possible arrangement would be :


^4C_3=(4!)/(3!* 1!)=(24)/(6)=4

1) We need to find the probability that Higgins forms a three letter arrangement with vowels as the second and third letters is as follows:

  • For the first letter to be not vowels is
    (2)/(4)
  • For the second letter to be vowel is
    (2)/(3)
  • For the third letter to be vowel is
    (1)/(2)

So, the total probability that a three letter arrangement with vowels as the second and third letters is


(2)/(4)* (2)/(3)* (1)/(2)=(4)/(24)=(1)/(6)

Therefore, Third option is correct.

Now, we need to find the probability that HIggins forms a three letter arrangement with two consecutive consonants is as follows:

  • For the first letter to be consonants is
    (2)/(4)
  • For the second letter to be consonant is
    (2)/(3)
  • For the third letter to be consonant is
    (2)/(2)

So, the Probability that Higgins forms a three letter arrangement with two consecutive consonants is given by


(2)/(4)* (2)/(3)* (2)/(2)=(8)/(24)=(1)/(3)

Hence, First option is correct.

User Degan
by
7.5k points

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