Question

Count all the ways to rearrange the letters in the word BRASIL.

Answer #1

Since, there are 6 letters & all are distinct, so if we rearrange them to make a 6letter word,

for 1st place, we have any of 6 possibilities= 6 ways

for 2nd place, we have all 5(except the one that we had used at 1st place) = 5waya

similarly for 3rd, 4th, 5th & 6th place, we have 4, 3, 2 & 1 ways respectively because the letters that had been used, can’t be used again so number of ways reduced by 1 every time.

So total number of words = 6*5*4*3*2*1 = 6! = 720

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).

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.

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?

1. How many permutations are there of the letters in the word
RINSE, if all the letters are used without repetition?
2. In how many distinct ways can the letters of the word SELLS
be arranged?

a. Find the number of ways to arrange the three letters in the
word CAT in different two-letter groups where CA is different from
AC and there are no repeated letters.
b. Three members from the group of 12 on the board of directors
at Belford Community Hospital will be selected to go to a
convention with all expenses paid. How many different groups of 3
are there?

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

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?

(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?

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?

Q6.
In how many different ways can the letters of the word
'MATHEMATICS' be arranged so that the vowels always come
together?

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