Advertisements
Advertisements
Question
The letters of the word 'FORTUNATES' are arranged at random in a row. What is the chance that the two 'T' come together.
Solution
There are 10 letters in the word ‘FORTUNATES’, which can be arranged in 10! ways.
There are two T's in the word.
Let us consider these two letters in the word ‘FORTUNATES’ as one letter.
So, when the two T's are clubbed together, we have (T,T) FORUNAES.
We can arrange 9 letters in a row in 9! ways.
Also, the two T's can themselves be arranged in 2! ways.
Hence, required probability = \[\frac{9! \times 2!}{10!} = \frac{9! \times 2}{10 \times 9!} = \frac{1}{5}\]
APPEARS IN
RELATED QUESTIONS
Describe the sample space for the indicated experiment: A coin is tossed three times.
An experiment consists of recording boy-girl composition of families with 2 children.
(i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?
(ii) What is the sample space if we are interested in the number of girls in the family?
An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.
What is the total number of elementary events associated to the random experiment of throwing three dice together?
2 boys and 2 girls are in room P and 1 boy 3 girls are in room Q. Write the sample space for the experiment in which a room is selected and then a person.
A die is thrown repeatedly until a six comes up. What is the sample space for this experiment.
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is either a black card or a king
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is neither a heart nor a king
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is neither an ace nor a king
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is not an ace
In shuffling a pack of 52 playing cards, four are accidently dropped; find the chance that the missing cards should be one from each suit.
From a deck of 52 cards, four cards are drawn simultaneously, find the chance that they will be the four honours of the same suit.
A bag contains 6 red, 4 white and 8 blue balls. if three balls are drawn at random, find the probability that one is red, one is white and one is blue.
A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that both the balls are white
A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that one ball is black and the other red
A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability that one is red and two are white
A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability that two are blue and one is red
Five cards are drawn from a pack of 52 cards. What is the chance that these 5 will contain at least one ace?
Five cards are drawn from a pack of 52 cards. What is the chance that these 5 will contain at least one ace?
20 cards are numbered from 1 to 20. One card is drawn at random. What is the probability that the number on the cards is divisible by 5?
A class consists of 10 boys and 8 girls. Three students are selected at random. What is the probability that the selected group has all boys?
A class consists of 10 boys and 8 girls. Three students are selected at random. What is the probability that the selected group has all girls?
A class consists of 10 boys and 8 girls. Three students are selected at random. What is the probability that the selected group has 1 boys and 2 girls?
A class consists of 10 boys and 8 girls. Three students are selected at random. What is the probability that the selected group has at least one girl?
A sample space consists of 9 elementary events E1, E2, E3, ..., E9 whose probabilities are
P(E1) = P(E2) = 0.08, P(E3) = P(E4) = P(E5) = 0.1, P(E6) = P(E7) = 0.2, P(E8) = P(E9) = 0.07
Suppose A = {E1, E5, E8}, B = {E2, E5, E8, E9}
Compute P(A), P(B) and P(A ∩ B).
A sample space consists of 9 elementary events E1, E2, E3, ..., E9 whose probabilities are
P(E1) = P(E2) = 0.08, P(E3) = P(E4) = P(E5) = 0.1, P(E6) = P(E7) = 0.2, P(E8) = P(E9) = 0.07
Suppose A = {E1, E5, E8}, B = {E2, E5, E8, E9}
Calculate \[P\left( \bar{ B} \right)\] from P(B), also calculate \[P\left( \bar{ B } \right)\] directly from the elementary events of \[\bar{ B } \] .
One card is drawn from a pack of 52 cards. The probability that it is the card of a king or spade is
Two dice are thrown simultaneously. The probability of obtaining total score of seven is
6 boys and 6 girls sit in a row at random. The probability that all the girls sit together is
Three digit numbers are formed using the digits 0, 2, 4, 6, 8. A number is chosen at random out of these numbers. What is the probability that this number has the same digits?
An ordinary deck of cards contains 52 cards divided into four suits. The red suits are diamonds and hearts and black suits are clubs and spades. The cards J, Q, and K are called face cards. Suppose we pick one card from the deck at random. What is the event that the chosen card is a black face card?
How many two-digit positive integers are multiples of 3?
Three of the six vertices of a regular hexagon are chosen at random. What is the probability that the triangle with these vertices is equilateral?
A bag contains 20 tickets numbered 1 to 20. Two tickets are drawn at random. The probability that both the numbers on the ticket are prime is ______.
