मराठी

How Many Words, with Or Without Meaning, Can Be Formed by Using the Letters of the Word 'Triangle'? - Mathematics

Advertisements
Advertisements

प्रश्न

How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?

Advertisements

उत्तर

There are 8 letters in the word TRIANGLE.
∴ Number of 8 letter words = Number of arrangements of 8 letters, taken 8 at a time
8P8 = 8!

shaalaa.com
Factorial N (N!) Permutations and Combinations
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 16: Permutations - Exercise 16.3 [पृष्ठ २८]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 16 Permutations
Exercise 16.3 | Q 22 | पृष्ठ २८

संबंधित प्रश्‍न

Convert the following products into factorials:

5 · 6 · 7 · 8 · 9 · 10


If P (5, r) = P (6, r − 1), find r ?


If nP4 = 360, find the value of n.


If P (n − 1, 3) : P (n, 4) = 1 : 9, find n.


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


If n +5Pn +1 =\[\frac{11 (n - 1)}{2}\]n +3Pn, find n.


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?


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


There are 6 items in column A and 6 items in column B. A student is asked to match each item in column A with an item in column B. How many possible, correct or incorrect, answers are there to this question?


How many 3-digit even number can be made using the digits 1, 2, 3, 4, 5, 6, 7, if no digits is repeated?


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 'STRANGE' be arranged so that

the vowels occupy only the odd places?


How many words can be formed from the letters of the word 'SUNDAY'? How many of these begin with D?


How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:

the vowels always occupy even places?


How many permutations can be formed by the letters of the word, 'VOWELS', when

there is no restriction on letters?


How many permutations can be formed by the letters of the word, 'VOWELS', when

each word begins with O and ends with L?


How many permutations can be formed by the letters of the word, 'VOWELS', when

all vowels come together?


m men and n women are to be seated in a row so that no two women sit together. if m > n then show that the number of ways in which they can be seated as\[\frac{m! (m + 1)!}{(m - n + 1) !}\]


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


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

INDIA


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

RUSSIA


How many words can be formed with the letters of the word 'UNIVERSITY', the vowels remaining together?


Find the total number of arrangements of the letters in the expression a3 b2 c4 when written at full length.


How many words can be formed with the letters of the word 'PARALLEL' so that all L's do not come together?


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


How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?


How many different signals can be made from 4 red, 2 white and 3 green flags by arranging all of them vertically on a flagstaff?


In how many ways can the letters of the word 'ARRANGE' be arranged so that the two R's are never together?


How many permutations of the letters of the word 'MADHUBANI' do not begin with M but end with I?


How many different arrangements can be made by using all the letters in the word 'MATHEMATICS'. How many of them begin with C? How many of them begin with T?


If the letters of the word 'MOTHER' are written in all possible orders and these words are written out as in a dictionary, find the rank of the word 'MOTHER'.


Prove that: 4nC2n : 2nCn = [1 · 3 · 5 ... (4n − 1)] : [1 · 3 · 5 ... (2n − 1)]2.


Evaluate

\[^ {20}{}{C}_5 + \sum^5_{r = 2} {}^{25 - r} C_4\]

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


There are 10 persons named\[P_1 , P_2 , P_3 , . . . . , P_{10}\]
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.


Write the number of diagonals of an n-sided polygon.


Write the expression nCr +1 + nCr − 1 + 2 × nCr in the simplest form.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×