Question

The letters of the word "REARRANGE" are randomly rearranged. What is the probability that this rearrangement has no consecutive vowels? Please explain why you use the formula you used.

Answer #1

A monkey, type words of three letters randomly on a
computer. Which is the
probability that you write a word formed by a consonant followed by
two vowels?
The word does not necessarily have to make sense. For simplicity
suppose that the keyboard It has 100 keys.

How many different ways can the letters in the word STATISTICS
be rearranged?
(Type your exact solution. Since this is a counting question,
your answer should be a whole number. Do not use comma's or
scientific notation)

1. In how many distinguishable ways can we rearrange the letters
in the word "conversationalists"?
2. A person is asked to draw one card from a standard deck of
(well-shuffled) cards, look at the card, place it back into the
deck, and then reshuffle the deck. If the experiment is repeated 5
times, find the probability of drawing the Ace of Clubs exactly
twice (out of the 5 draws).

What is the probability of these events when we randomly select
a permutation of the 26 lowercase letters of the English alphabet?
(a) a is the first letter of the permutation and z is the last
letter. (b) The 5 vowels are not all separated. (c) The first 3
letters are all together in the permutation (in some order) or the
last 4 letters are all together in the permutation (in some order).
(d) The first 13 letters of the...

The Hawaiian alphabet has twelve letters: five vowels (a, e, i,
o, and u) and seven consonants (h, k, l, m, n, p, and w). For the
purpose of this exercise we will define an n–letter “word” as an
ordered collection of n of these twelve letters with repeats
allowed. Obviously, most such “words” will be nonsense words.
What is the probability a randomly selected four–letter “word”
contains exactly one consonant?

4. The Hawaiian alphabet has twelve letters: five vowels (a, e,
i, o, and u) and seven consonants (h, k, l, m, n, p, and w). For
the purpose of this exercise we will define an n–letter “word” as
an ordered collection of n of these twelve letters with repeats
allowed. Obviously, most such “words” will be nonsense words.
e) What is the probability a randomly selected
four–letter “word” contains exactly one consonant?

Two coins are tossed. If two heads are thrown, letters are
chosen from the word TWOFOLD. If one head is thrown, letters are
chosen from the word ONEROUS. If no heads are thrown, letters are
chosen from the word NOMAD. Whichever word is used, we draw letters
one at a time, without replacement, until a vowel is obtained. What
is the expected number of letters then drawn?
Answer is 59/30. Please show each steps clearly and
specifically. Thank you.

What is the probability that a randomly chosen four letter word
will begin with HA
0.5
0.032519631
0.001479289941
0.03846153846
0.0000021883

16. An individual is heterozygous for a chromosomal
rearrangement. A normal chromosome and its aberrant homolog are
given below, where the dot represents the centromere: Normal
ABC:DEFGHI Aberrant afed.cbghi What type of chromosomal
rearrangement is being shown in the aberrant chromosome? Be
specific.
17. An individual is heterozygous for a chromosomal rearrangement.
A normal chromosome and its aberrant homolog are given below, where
the dot represents the centromere: Normal ABC:DEFGHI Aberrant
afed.cbghi What are the recombinant chromosomes that are produced...

Suppose that you have 20 different letters and 10 distinctly
addressed envelopes. The 20letters consist of 10 pairs, where each
pair belongs inside one of the 10 envelopes. Suppose that you place
the 20letters inside the 10 envelopes, two per envelope, but at
random. What is the probability that exactly 3 of the 10 envelopes
will contain both of the letters which they should contain?
I know the answer is [ (20-2*3)! / 2^(10-3) ] / [20! / 2^10] but...

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