Advertisements
Advertisements
प्रश्न
The number of arrangements of the letters of the word BHARAT taking 3 at a time is
पर्याय
72
120
14
none of these.
उत्तर
72
When we make words after selecting letters of the word BHARAT, it could consist of a single A, two As or no A.
Case-I: A is not selected for the three letter word.
Number of arrangements of three letters out of B, H, R and T =\[4 \times 3 \times 2\]
Case-II: One A is selected and the other two letters are selected out of B, H, R or T.
Possible ways of selection: Selecting two letters out of B, H, R or T can be done in \[^{4}{}{P}_2\]
=12 ways.
Now, in each of these 12 ways, these two letters can be placed at any of the three places in the three letter word in 3 ways.
∴ Total number of words that can be formed = 12 x 3 = 36
Case-III: Two A's and a letter from B, H, R or T are selected.
Possible ways of arrangement:
Number of ways of selecting a letter from B, H, R or T = 4
And now this letter can be placed in any one of the three places in the three letter word other than the two A's in 3 ways.
∴ Total number of words having 2 A's = 4 x 3 =12
Hence, total number of words that can be formed = 24 + 36 + 12 = 72
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?
How many 4-digit numbers are there with no digit repeated?
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
Find r if `""^5P_r = ""^6P_(r-1)`
How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
(i) 4 letters are used at a time,
(ii) all letters are used at a time,
(iii) all letters are used but first letter is a vowel?
In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together.
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
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?
How many natural numbers less than 1000 can be formed from the digits 0, 1, 2, 3, 4, 5 when a digit may be repeated any number of times?
Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.
In how many ways can 7 letters be posted in 4 letter boxes?
Write the total number of possible outcomes in a throw of 3 dice in which at least one of the dice shows an even number.
Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together ?
Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?
The number of six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters is
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.
If (n+2)! = 60[(n–1)!], find n
If nP4 = 12(nP2), find n.
Evaluate the following.
`(3! + 1!)/(2^2!)`
The total number of 9 digit number which has all different digit is:
The number of ways to arrange the letters of the word “CHEESE”:
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if question number n has n + 1 choices?
In how many ways can the letters of the word SUCCESS be arranged so that all Ss are together?
A coin is tossed 8 times, how many different sequences of heads and tails are possible?
How many strings are there using the letters of the word INTERMEDIATE, if all the vowels are together
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 distinct 6-digit numbers are there?
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
GARDEN
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 0, 2, 5, 7, 8 without repetition?
How many words can be formed with the letters of the word MANAGEMENT by rearranging them?
In how many ways can 5 children be arranged in a line such that two particular children of them are never together.
Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is ______.
The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.
The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
