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
Evaluate 8!
Evaluate 4! – 3!
Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5
How many 4-digit numbers are there with no digit repeated?
In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
Find x in each of the following:
Find x in each of the following:
A customer forgets a four-digits code for an Automatic Teller Machine (ATM) in a bank. However, he remembers that this code consists of digits 3, 5, 6 and 9. Find the largest possible number of trials necessary to obtain the correct code.
A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there? How many possible outcomes if the coin is tossed four times? Five times? n times?
How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?
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 ?
Evaluate each of the following:
8P3
In how many ways can 4 letters be posted in 5 letter boxes?
Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?
The number of arrangements of the word "DELHI" in which E precedes I is
Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is
If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is
The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is
The product of r consecutive positive integers is divisible by
The number of arrangements of the letters of the word BHARAT taking 3 at a time is
The number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, is
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
Evaluate the following.
`(3! + 1!)/(2^2!)`
Evaluate the following.
`((3!)! xx 2!)/(5!)`
If n is a positive integer, then the number of terms in the expansion of (x + a)n is:
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together
How many strings are there using the letters of the word INTERMEDIATE, if no two vowels are together
If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
DANGER
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
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?
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
Let b1, b2, b3, b4 be a 4-element permutation with bi ∈ {1, 2, 3, .......,100} for 1 ≤ i ≤ 4 and bi ≠ bj for i ≠ j, such that either b1, b2, b3 are consecutive integers or b2, b3, b4 are consecutive integers. Then the number of such permutations b1, b2, b3, b4 is equal to ______.
If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ______.
