Question

How many ways can you order the letters of DABALA if it begins with exactly 2 A’s?

Answer #1

How many ways can we order the letters in SEVENTEEN? (Hint: Not
all of the letters are distinct, so the plain permutations formula
does not apply.)

2. (a) In how many ways, can you arrange the letters in the word
“Massachusetts”?
(b) Let’s introduce an additional constraint: a vowel letter has
to be the first letter in your arrangement. How many ways can you
arrange these letters now?

How many distinguishable ways can the letters of the word
COMMUNICATION be arranged in order?

Permutations---------
In how many distinct ways can all the letters of the word
UNBELIEVABLE be arranged amongst themselves if
a) there are no restrictions?
b) the arrangement begins with the letters I V A, in that
order?
c) the arrangements must begin and end with a consonant?

(a) In how many ways, can you arrange the letters in the word
“Massachusetts”?
(b) Let’s introduce an additional constraint: a vowel letter has
to be the first letter in your arrangement. How many ways can you
arrange these letters now?

In how many ways can the letters in the word
TRAPEZOIDS be arranged:
a) if you must use 6 different letters?
b) if you use any 6 letters and repetitions are allowed?
c) if the six-letter arrangement must start and end with a
consonant, and repetitions are not allowed?

How many ways are there to select 6 different letters out of 26
letters of the alphabet?
2. How many strings of 6 letters are there – if the letters
cannot be repeated?
3. How many strings of 6 letters are there – if the letters can
be repeated?

Suppose we want to choose 5 letters, without replacement, from
13 distinct letters.
How many ways can this be done, if the order of the choices does
not matter?
How many ways can this be done, if the order of the choices
matters?

How
many ways can a license plate be generated if you have three
letters and two numbers in the plate and you are not allowed to
repeat the letters nor the number?

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).

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