Advertisements
Advertisements
प्रश्न
Write the number of words that can be formed out of the letters of the word 'COMMITTEE' ?
Advertisements
उत्तर
The word COMMITTEE consists of 9 letters including two Ms, two Ts and two Es.
Number of words that can be formed out of the letters of the word COMMITTEE
= Number of arrangements of 9 things of which 2 are similar to the first kind,
2 are similar to the second kind and 2 are similar to the third kind =\[\frac{9!}{2!2!2!} = \frac{9!}{\left( 2! \right)^3}\]
APPEARS IN
संबंधित प्रश्न
Is 3! + 4! = 7!?
if `1/(6!) + 1/(7!) = x/(8!)`, find x
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
Find r if `""^5P_r = ""^6P_(r-1)`
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
Find x in each of the following:
Find x in each of the following:
Which of the following are true:
(2 × 3)! = 2! × 3!
In how many ways can three jobs I, II and III be assigned to three persons A, B and C if one person is assigned only one job and all are capable of doing each job?
Find the number of ways in which one can post 5 letters in 7 letter boxes ?
In how many ways can 7 letters be posted in 4 letter boxes?
In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes?
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated ?
In how many ways can 4 letters be posted in 5 letter boxes?
In how many ways 4 women draw water from 4 taps, if no tap remains unused?
Write the number of arrangements of the letters of the word BANANA in which two N's come together.
Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.
The number of different signals which can be given from 6 flags of different colours taking one or more at a time, is
The number of arrangements of the word "DELHI" in which E precedes I is
A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is
How many 6-digit telephone numbers can be constructed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each numbers starts with 35 and no digit appear more than once?
Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.
Find the rank of the word ‘CHAT’ in the dictionary.
The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
Find the distinct permutations of the letters of the word MISSISSIPPI?
How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many of these 6-digit numbers are divisible by 4?
If the letters of the word FUNNY are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, find the rank of the word FUNNY
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
Choose the correct alternative:
If Pr stands for rPr then the sum of the series 1 + P1 + 2P2 + 3P3 + · · · + nPn is
How many words can be formed with the letters of the word MANAGEMENT by rearranging them?
Three married couples are to be seated in a row having six seats in a cinema hall. If spouses are to be seated next to each other, in how many ways can they be seated? Find also the number of ways of their seating if all the ladies sit together.
There are 10 persons named P1, P2, P3, ... P10. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:
| C1 | C2 |
| (a) Boys and girls alternate: | (i) 5! × 6! |
| (b) No two girls sit together : | (ii) 10! – 5! 6! |
| (c) All the girls sit together | (iii) (5!)2 + (5!)2 |
| (d) All the girls are never together : | (iv) 2! 5! 5! |
