Advertisements
Advertisements
Question
If the letters of the word RACHIT are arranged in all possible ways as listed in dictionary. Then what is the rank of the word RACHIT?
Advertisements
Solution
The alphabetical order of RACHIT is A, C, H, I, R and T
Number of words beginning with A = 5!
Number of words beginning with C = 5!
Number of words beginning with H = 5!
Number of words beginning with I = 5!
And Number of word beginning with R i.e. RACHIT = 1
∴ The rank of the word ‘RACHIT’ in the dictionary
= 5! + 5! + 5! + 5! + 1
= 4 × 5! + 1
= 4 × 5 × 4 × 3 × 2 × 1 + 1
= 4 x 120 + 1
= 480 + 1
= 481
APPEARS IN
RELATED QUESTIONS
Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?
How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits are not allowed?
A letter lock contains 3 rings, each ring containing 5 different letters. Determine the maximum number of false trials that can be made before the lock is opened?
How many numbers between 100 and 1000 have 4 in the units place?
How many numbers between 100 and 1000 have the digit 7 exactly once?
If numbers are formed using digits 2, 3, 4, 5, 6 without repetition, how many of them will exceed 400?
Select the correct answer from the given alternatives.
A college has 7 courses in the morning and 3 in the evening. The possible number of choices with the student if he wants to study one course in the morning and one in the evening is -
A person went to a restaurant for dinner. In the menu card, the person saw 10 Indian and 7 Chinese food items. In how many ways the person can select either an Indian or a Chinese food?
There are 3 types of toy car and 2 types of toy train available in a shop. Find the number of ways a baby can buy a toy car and a toy train?
Four children are running a race:
In how many different ways could they finish the race?
Count the number of three-digit numbers which can be formed from the digits 2, 4, 6, 8 if repetitions of digits is allowed
How many three-digit odd numbers can be formed by using the digits 0, 1, 2, 3, 4, 5? if the repetition of digits is not allowed
Count the numbers between 999 and 10000 subject to the condition that there are no digit is repeated
How many three-digit numbers, which are divisible by 5, can be formed using the digits 0, 1, 2, 3, 4, 5 if repetition of digits are allowed?
To travel from a place A to place B, there are two different bus routes B1, B2, two different train routes T1, T2 and one air route A1. From place B to place C there is one bus route say B1, two different train routes say T1, T2 and one air route A1. Find the number of routes of commuting from place A to place C via place B without using similar mode of transportation
How many numbers are there between 1 and 1000 (both inclusive) which are divisible neither by 2 nor by 5?
In how many ways 10 pigeons can be placed in 3 different pigeon holes?
Find the value of 6!
Find the value of 3! × 2!
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 6, r = 2
Find the value of n if `1/(8!) + 1/(9!) = "n"/(10!)`
In a class, there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent the class for a function. In how many ways can the teacher make this selection?
How many numbers are there between 99 and 1000 having 7 in the units place?
In how many ways can this diagram be coloured subject to the following two conditions?
(i) Each of the smaller triangle is to be painted with one of three colours: red, blue or green.
(ii) No two adjacent regions have the same colour.
A candidate is required to answer 7 questions out of 12 questions, which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing question
Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the point
Find the number of positive integers greater than 6000 and less than 7000 which are divisible by 5, provided that no digit is to be repeated.
The sum of the digits in unit place of all the numbers formed with the help of 3, 4, 5 and 6 taken all at a time is ______.
In a steamer there are stalls for 12 animals, and there are horses, cows and calves (not less than 12 each) ready to be shipped. They can be loaded in 312 ways.
There will be only 24 selections containing at least one red ball out of a bag containing 4 red and 5 black balls. It is being given that the balls of the same colour are identical.
If the number of five-digit numbers with distinct digits and 2 at the 10th place is 336 k, then k is equal to ______.
