Advertisements
Advertisements
प्रश्न
Solve the following:
In how many ways can the letters of the word ARRANGEMENTS be arranged? Find the chance that an arrangement chosen at random begins with the letters EE.
उत्तर
The word ‘ARRANGEMENTS’ has 12 letters in which 2A, 2E, 2N, 2R, G, M, T, S are there.
n(S) = Total number of arrangements
= `(12!)/(2! 2! 2! 2!)`
= `(12!)/(2!)^4`
A: Arrangement chosen at random begins with the letters EE.
If the first and second places are filled with EE, there are 10 letters left in which 2A, 2N, 2R, G, M, T, S are there.
∴ n(A) = `(10!)/(2!2!2!)`
= `(10!)/(2!)^3`
∴ P(A) = `("n"("A"))/("n"("S"))`
= `(10!)/(2!)^3 xx (2!)^4/(12!)`
= `2/(12 xx 11)`
= `1/66`
APPEARS IN
संबंधित प्रश्न
There are four pens: Red, Green, Blue, and Purple in a desk drawer of which two pens are selected at random one after the other with replacement. State the sample space and the following event.
A: Selecting at least one red pen.
There are four pens: Red, Green, Blue, and Purple in a desk drawer of which two pens are selected at random one after the other with replacement. State the sample space and the following event.
B: Two pens of the same color are not selected.
A coin and a die are tossed simultaneously. Enumerate the sample space and the following event.
B: Getting a prime number
Find n(S) of the following random experiment.
From an urn containing 5 gold and 3 silver coins, 3 coins are drawn at random
Find n(S) of the following random experiment.
5 letters are to be placed into 5 envelopes such that no envelope is empty.
Find n(S) of the following random experiment.
6 books of different subjects arranged on a shelf.
Two fair dice are thrown. State the sample space and write favorable outcomes for the following event:
B: Sum of numbers on two dice is 7
Two fair dice are thrown. State the sample space and write favorable outcomes for the following event:
C: Odd number on the first die.
Two fair dice are thrown. State the sample space and write favorable outcomes for the following event:
D: Even number on the first die.
Two fair dice are thrown. State the sample space and write favorable outcomes for the following events:
Check whether events A and B are mutually exclusive and exhaustive.
A: Sum of numbers on two dice is divisible by 3 or 4.
B: Sum of numbers on two dice is 7.
A bag contains four cards marked as 5, 6, 7, and 8. Find the sample space if two cards are drawn at random with replacement.
From a bag containing 10 red, 4 blue and 6 black balls, a ball is drawn at random. Find the probability of drawing a red ball.
From a bag containing 10 red, 4 blue and 6 black balls, a ball is drawn at random. Find the probability of drawing a blue or black ball
A box contains 75 tickets numbered 1 to 75. A ticket is drawn at random from the box. Find the probability that, Number on the ticket is a perfect square
A box contains 75 tickets numbered 1 to 75. A ticket is drawn at random from the box. Find the probability that, Number on the ticket is divisible by 3 and 5
What is the chance that a leap year, selected at random, will contain 53 Sundays?
A room has three sockets for lamps. From a collection 10 bulbs of which 6 are defective. At night a person selects 3 bulbs, at random and puts them in sockets. What is the probability that room is still dark
Select the correct option from the given alternatives :
In a jar there are 5 black marbles and 3 green marbles. Two marbles are picked randomly one after the other without replacement. What is the possibility that both the marbles are black?
Select the correct option from the given alternatives :
In a set of 30 shirts, 17 are white and rest are black. 4 white and 5 black shirts are tagged as ‘PARTY WEAR’. If a shirt is chosen at random from this set, the possibility of choosing a black shirt or a ‘PARTY WEAR’ shirt is
Solve the following:
The letters of the word 'EQUATION' are arranged in a row. Find the probability that All the vowels are together
Solve the following:
The letters of the word 'EQUATION' are arranged in a row. Find the probability that Arrangement starts with a vowel and ends with a consonant
Solve the following:
Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is and even number?
Solve the following:
If the letters of the word 'REGULATIONS' be arranged at random, what is the probability that there will be exactly 4 letters between R and E?
Solve the following:
A letter is taken at random from the letters of the word 'ASSISTANT' and another letter is taken at random from the letters of the word 'STATISTICS'. Find the probability that the selected letters are the same
If three fair coins are tossed, where X = number of tails obtained, then Var(X) is ______
Three randomly chosen non-negative integer x, y and z are found to satisfy the equation x + y + z = 10. Then, the probability that z is even, is ______.
Two events A and B have probabilities 0.25 and 0.50, respectively. The probability that both A and B occur simultaneously is 0.14. Then, the probability that neither A nor B occurs, is ______.
