Advertisements
Advertisements
प्रश्न
The letters of the word LOGARITHM are arranged at random. Find the probability that vowels are always together.
Advertisements
उत्तर
There are 9 letters in the word LOGARITHM.
These letters can be arranged among themselves in 9P9 = 9! ways.
∴ n(S) = 9!
Let A be the event that vowels are always together.
The word LOGARITHM consists of 3 vowels (O, A, I) and 6 consonants (L, G, R, T, H, M).
3 vowels can be arranged among themselves in = 3P3 = 3! ways.
Considering 3 vowels as one group, 6 consonants and this group (i.e., altogether 7) can be arranged in 7P7 = 7! ways.
∴ n(A) = 7! × 3!
∴ P(A) = `("n"("A"))/("n"("S"))`
= `(7!xx3!)/(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 at least 10.
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 3 are king and 1 is jack.
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 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 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 never together.
The letters of the word LOGARITHM are arranged at random. Find the probability that Exactly 4 letters between G and H.
The letters of the word LOGARITHM are arranged at random. Find the probability that start with vowel and end with ends with consonant.
