Advertisements
Advertisements
प्रश्न
The letters of the word LOGARITHM are arranged at random. Find the probability that vowels are never together.
उत्तर
There are 9 letters in the word LOGARITHM.
These letters can be arranged among themselves in 9P9 = 9! ways
∴ n(S) = 9!
There are 9 letters in the word LOGARITHM.
These letters can be arranged among themselves in 9 P9 = 9! ways
C C C C C C
6 consonants create 7 gaps.
∴ 3 vowels can be arranged in 7 gaps in 7P3 ways. Also 6 consonants can be arranged among themselves in 6P6 = 6! ways.
∴ n(B) = 6! x `""^7"P"_3`
∴ P(B) = `("n"("B"))/("n"("S")`
= `(6! xx""^7"P"_3)/(9!)`
APPEARS IN
संबंधित प्रश्न
A fair die is thrown two times. Find the chance that product of the numbers on the upper face is 12.
A fair die is thrown two times. Find the chance that sum of the numbers on the upper face is 10.
A fair die is thrown two times. Find the chance that both the times die shows same number (doublet).
Two cards are drawn from a pack of 52 cards. Find the probability that both are black.
Two cards are drawn from a pack of 52 cards. Find the probability that both are diamonds.
Two cards are drawn from a pack of 52 cards. Find the probability that both are ace cards.
Two cards are drawn from a pack of 52 cards. Find the probability that both are from same suit.
Two cards are drawn from a pack of 52 cards. Find the probability that both are from same denomination.
Four cards are drawn from a pack of 52 cards. Find the probability that all cards are club and one of them a jack.
A bag contains 15 balls of three different colours: Green, Black and Yellow. A ball is drawn at random from the bag. The probability of green ball is `1/3`. The probability of yellow ball is `1/5`. What is the probability of blackball?
A bag contains 15 balls of three different colours: Green, Black and Yellow. A ball is drawn at random from the bag. The probability of green ball is `1/3`. The probability of yellow ball is `1/5`. How many balls are green, black, and yellow?
A box contains 75 tickets numbered 1 to 75. A ticket is drawn at random from the box. What is the probability that, number on ticket is divisible by 6?
A box contains 75 tickets numbered 1 to 75. A ticket is drawn at random from the box. What is the probability that, number on ticket is a perfect square?
A box contains 75 tickets numbered 1 to 75. A ticket is drawn at random from the box. What is the probability that, number on ticket is divisible by 3 and 5?
From a group of 8 boys and 5 girls, a committee of five is to be formed. Find the probability that the committee contains at least 3 boys.
A room has three sockets for lamps. From a collection of 10 light bulbs of which 6 are defective, a person selects 3 bulbs at random and puts them in socket. What is the probability that the room is lit?
The letters of the word LOGARITHM are arranged at random. Find the probability that vowels are always together.
The letters of the word LOGARITHM are arranged at random. Find the probability that Begins with O and ends with T.
