हिंदी

How Many Three Letter Words Can Be Made Using the Letters of the Word 'Oriental'?

Advertisements
Advertisements

प्रश्न

How many three letter words can be made using the letters of the word 'ORIENTAL'?

Advertisements

उत्तर

The word ORIENTAL consists of 8 letters. In order to make three letter words, we need to permute these 8 letters, taken three at a time.
⇒ 8P3 = 8\[\times\]7\[\times\]6 = 336

shaalaa.com
Factorial N (N!) Permutations and Combinations
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 16: Permutations - Exercise 16.4 [पृष्ठ ३७]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 16 Permutations
Exercise 16.4 | Q 12 | पृष्ठ ३७

संबंधित प्रश्न

If (n + 1)! = 90 [(n − 1)!], find n.


Prove that:

\[\frac{(2n + 1)!}{n!}\] = 2n [1 · 3 · 5 ... (2n − 1) (2n + 1)]

If 5 P(4, n) = 6. P (5, n − 1), find n ?


If P (n, 5) = 20. P(n, 3), find n ?


If nP4 = 360, find the value of n.


If P (9, r) = 3024, find r.


If P (n, 4) = 12 . P (n, 2), find n.


If P (n, 5) : P (n, 3) = 2 : 1, find n.


Prove that:1 . P (1, 1) + 2 . P (2, 2) + 3 . P (3, 3) + ... + n . P (nn) = P (n + 1, n + 1) − 1.


If P (15, r − 1) : P (16, r − 2) = 3 : 4, find r.


From among the 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?


Four letters E, K, S and V, one in each, were purchased from a plastic warehouse. How many ordered pairs of letters, to be used as initials, can be formed from them?


Find the number of different 4-letter words, with or without meanings, that can be formed from the letters of the word 'NUMBER'.


All the letters of the word 'EAMCOT' are arranged in different possible ways. Find the number of arrangements in which no two vowels are adjacent to each other.


In how many ways can the letters of the word 'FAILURE' be arranged so that the consonants may occupy only odd positions?


In how many ways can the letters of the word 'STRANGE' be arranged so that

the vowels never come together? 


In how many ways can the letters of the word 'STRANGE' be arranged so that

the vowels occupy only the odd places?


How many different words can be formed with the letters of word 'SUNDAY'? How many of the words begin with N? How many begin with N and end in Y?


Find the number of words formed by permuting all the letters of the following words:
INTERMEDIATE


Find the number of words formed by permuting all the letters of the following words:

PAKISTAN


Find the number of words formed by permuting all the letters of the following words:

RUSSIA


Find the number of words formed by permuting all the letters of the following words:
CONSTANTINOPLE


How many words can be formed by arranging the letters of the word 'MUMBAI' so that all M's come together?


How many different numbers, greater than 50000 can be formed with the digits 0, 1, 1, 5, 9.


There are three copies each of 4 different books. In how many ways can they be arranged in a shelf?


A biologist studying the genetic code is interested to know the number of possible arrangements of 12 molecules in a chain. The chain contains 4 different molecules represented by the initials A (for Adenine), C (for Cytosine), G (for Guanine) and T (for Thymine) and 3 molecules of each kind. How many different such arrangements are possible?


In how many ways can 4 red, 3 yellow and 2 green discs be arranged in a row if the discs of the same colour are indistinguishable?


In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?


If the letters of the word 'LATE' be permuted and the words so formed be arranged as in a dictionary, find the rank of the word LATE.


If the permutations of a, b, c, d, e taken all together be written down in alphabetical order as in dictionary and numbered, find the rank of the permutation debac ?


In how many ways can the letters of the word
"INTERMEDIATE" be arranged so that:the vowels always occupy even places?


Prove that the product of 2n consecutive negative integers is divisible by (2n)!


Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
n · n − 1Cr − 1 = (n − r + 1) nCr − 1


Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:

\[\frac{^{n}{}{C}_r}{^{n - 1}{}{C}_{r - 1}} = \frac{n}{r}\]

Write the number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.


Write the number of ways in which 5 red and 4 white balls can be drawn from a bag containing 10 red and 8 white balls.


Write the number of ways in which 12 boys may be divided into three groups of 4 boys each.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×