मराठी

How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY, assuming that no letter is repeated, if 4 letters are used at a time?

Advertisements
Advertisements

प्रश्न

How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY, assuming that no letter is repeated, if 4 letters are used at a time?

थोडक्यात उत्तर
Advertisements

उत्तर

There are total 6 letters in the word MONDAY.

Total number of words by taking 4 letters out of 6 at a time = `""^("6")"P"_4` = 6 x 5 x 4 x 3 = 360 whereas words can be with or without meaning.

shaalaa.com
Factorial N (N!) Permutations and Combinations
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Permutations and Combinations - EXERCISE 6.3 [पृष्ठ ११४]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
पाठ 6 Permutations and Combinations
EXERCISE 6.3 | Q 9. (i) | पृष्ठ ११४
आर.डी. शर्मा Mathematics [English] Class 11
पाठ 16 Permutations
Exercise 16.4 | Q 11.1 | पृष्ठ ३७

संबंधित प्रश्‍न

If \[\frac{(2n)!}{3! (2n - 3)!}\]  and \[\frac{n!}{2! (n - 2)!}\]  are in the ratio 44 : 3, find n.

 

 


Prove that: 

\[\frac{n!}{(n - r)!}\] = n (n − 1) (n − 2) ... (n − (r − 1))

If P (5, r) = P (6, r − 1), find r ?


If P (9, r) = 3024, find r.


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?


How many three-digit numbers are there, with distinct digits, with each digit odd?


How many words, with or without meaning, can be formed by using all the letters of the word 'DELHI', using each letter exactly once?


How many three-digit numbers are there, with no digit repeated?


In how many ways can 6 boys and 5 girls be arranged for a group photograph if the girls are to sit on chairs in a row and the boys are to stand in a row behind them?


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
each word begins with E?


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?


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

all consonants come together?


How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY, assuming that no letter is repeated, if all letters are used at a time.


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:

RUSSIA


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


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?


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?


How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?


The letters of the word 'SURITI' are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word 'SURITI'.


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.


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)!


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


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

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

How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if (i) 4 letters are used at a time 


Find the number of permutations of n different things taken r at a time such that two specified things occur together?


If 35Cn +7 = 35C4n − 2 , then write the values of n.


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


Write the value of\[\sum^6_{r = 1} \ ^{56 - r}{}{C}_3 + \ ^ {50}{}{C}_4\]


Write the maximum number of points of intersection of 8 straight lines in a plane.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×