Arranging all the Letters of a Word where all the letters are different

No. Problems & Solutions [Click Hide/Show to display the solutions below the question]
01.
The letters of the word TRIANGLE are arranged at random. Find the probability and odds that the word so formed (i) starts with T (ii) ends with R (iii) starts with T and ends with R.

Solution
[1/8, 1/8, 1/56; 1:7, 7:1]

02.
The letters of the word ‘ORIENTAL’ are arranged in all possible ways. Find the probability and odds of getting an arrangement which starts with an vowel and ends with a consonant.

Solution
[1/8, 1/8, 1/56; 1:7, 7:1]

03.
In a random arrangement of the letters of the word “uncopyrightable”. Find (a) the probability and odds that all the vowels come together and (b) the probability that the vowels do not come together

Solution
[1/273, 1 : 272, 272:1; 272:273]

04.
Define the Event and identify the number of favourable choices in the following cases
a) The letters of the word SLAUGHTER are arranged in a row at random. Find the probability that the vowels may be in the odd places.
b) The letters of the word "RIGHTEOUSLY" are arranged in a row at random. Find the probability that the even places are filled with consonants.
c) The letters of the word “PENTAGON” are arranged in a row at random. Find the probability that there are exactly two letters between E and A is
d) Each of the letters A, B, E, L, T are written on a separate card. If all the cards are arranged in a row in all possible ways, the probability of the forming the word TABLE is

Solution
[1/273, 1 : 272, 272:1; 272:273]

No. Problems for Practice
01.
The letters of the word 'QUESTION' are arranged in a row at random. The probability that the word so formed starts with T and ends with N is
02.
The letters of 'EQUATION' are arranged in all positive ways. Find the probability of getting an arrangement which start with an vowel and ends with a consonant.
03.
a) The letters of the word TROPICAL are arranged in a row at random. Find the probability that no two vowels may come together.
b) The letters of the word VICTORY are arranged in a row at random. Find the probability that no two vowels may come together.
04.
a) The letters of the word TUESDAY are arranged in a row at random. The probability that there are exactly two letters between T and R.
b) The letters of the word QUESTION are arranged in a row at random. The probability that there are exactly two letters between Q and S.
c) The letters of the word EQUATION are arranged in a row at random. The probability that there are exactly two letters between E and A.
d) The letters of the word QUESTION are arranged in a row at random. The probability that there are exactly two letters between Q and N.
e) The letters of the word RANDOM are arranged in a row at random. The probability that there are exactly two letters between A and O.
05.
a) The letters of the word QUACKERY are arranged at random. Find the probability that the odd places are occupied by constants.
b) The letters of the word FAILURE are arranged at random. Find the probability that the vowels may occupy odd positions.
c) The letters of the word WRESTLING are arranged in a row at random. The probability that the vowels may be in even places is
e) The letters of the word ARTICLE are arranged at random. Find the probability that the constants may occupy odd places.
f) The letters of the word VICTORY are arranged in a row at random. The probability that the vowels may be in even places is
g) The letters of the word FAILURE are arranged at random. Find the probability that the vowels may occupy odd positions.
h) The letters of the word TUESDAY are arranged in a row at random. Find the probability that the vowels may be in the odd places.
i) The letters of the word EQUATION are arranged in a row at random. Find the probability that the consonants may be in the even places.
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