Question:medium

Let $S$ be the set of all words formed by arranging all the letters of the word HOMOGENEOUS. If a word is randomly chosen from the set $S$, then the probability that the word selected has all the consonants together is

Show Hint

When several letters must stay together, treat them as a single block first. Arrange the block with the remaining letters and then multiply by the internal arrangements of the letters within the block.

Updated On: Jul 29, 2026

$\dfrac{6!\,6!}{11!}$
$\dfrac{7!\,5!}{11!}$
$\dfrac{6!\,5!}{11!}$
$\dfrac{8!\,5!}{11!}$

Show Solution

The Correct Option is B

Solution and Explanation

Was this answer helpful?

Questions Asked in AP EAPCET exam

Let \[ f(x)=\int \frac{\sqrt{x}}{(1+x)^2}\,dx \quad (x\geq 0) \] Then \[ f(3)-f(1) \] is equal to:

AP EAPCET - 2026
Definite and indefinite integrals

View Solution

Gas is being pumped into a spherical balloon at the rate of $ 30 \, \text{ft}^3/\text{min} $. Then the rate at which the radius increases when it reaches the value $ 15 \, \text{ft} $ is:

AP EAPCET - 2026
Differentiation

View Solution

Let the function $ f(x) $ be defined as $ f(x) = \frac{x - |x|}{x} $, then:

AP EAPCET - 2026
Definite and indefinite integrals

View Solution

If the direction ratios of two lines are given by $ l + m + n = 0 $ and $ mn - 2ln + lm = 0 $, then the angle between the lines is:

AP EAPCET - 2026
3D Geometry

View Solution

Let \(S\) be the set of all words formed by arranging all the letters of the word HOMOGENEOUS. If a word is randomly chosen from the set \(S\), then the probability that the word selected has all the consonants together is

Show Hint

The Correct Option is B

Solution and Explanation

Top Questions on Probability

Questions Asked in AP EAPCET exam