हिंदी

In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S. - Mathematics

Advertisements
Advertisements

प्रश्न

In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S.

योग
Advertisements

उत्तर

The word PERMUTATIONS has a total 12 letters, in which T – 2, rest all are different.

The positions of P and S have been fixed.

Hence, in this case, required number of arrangements  

= `(10!)/(2!)` = 1814400.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 7: Permutations and Combinations - Exercise 7.3 [पृष्ठ १४८]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
अध्याय 7 Permutations and Combinations
Exercise 7.3 | Q 11.1 | पृष्ठ १४८

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Evaluate 8!


Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5


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?


Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?


From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?


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?


Which of the following are true:

(2 +3)! = 2! + 3!


In how many ways can three jobs I, II and III be assigned to three persons AB and C if one person is assigned only one job and all are capable of doing each job?


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?


In how many ways can 7 letters be posted in 4 letter boxes?


Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is


Evaluate the following.

`((3!)! xx 2!)/(5!)`


The possible outcomes when a coin is tossed five times:


For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:


The number of ways to arrange the letters of the word “CHEESE”:


The number of permutation of n different things taken r at a time, when the repetition is allowed is:


If `""^(("n"  – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n


A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?


How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative


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
GARDEN


Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?


Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?


Choose the correct alternative:
The product of r consecutive positive integers is divisible b


The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently is ______.


In how many ways can 5 children be arranged in a line such that two particular children of them are never together.


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 ______.


The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.


Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:

C1 C2
(a) Boys and girls alternate: (i) 5! × 6!
(b) No two girls sit together : (ii) 10! – 5! 6!
(c) All the girls sit together (iii) (5!)2 + (5!)2
(d) All the girls are never together : (iv) 2! 5! 5!

Using the digits 1, 2, 3, 4, 5, 6, 7, a number of 4 different digits is formed. Find

C1 C2
(a) How many numbers are formed? (i) 840
(b) How many number are exactly divisible by 2? (i) 200
(c) How many numbers are exactly divisible by 25? (iii) 360
(d) How many of these are exactly divisible by 4? (iv) 40

The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is ______.


Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Determine the number of words which have at least one letter repeated.


If m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.


8-digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do no occupy odd places is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×