मराठी

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.

बेरीज

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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: Permutations and Combinations - Exercise 7.3 [पृष्ठ १४८]

APPEARS IN

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

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Evaluate 8!


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?


Find r if `""^5P_r = 2^6 P_(r-1)`


In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?


How many numbers of six digits can be formed from the digits 0, 1, 3, 5, 7 and 9 when no digit is repeated? How many of them are divisible by 10 ?


If three six faced die each marked with numbers 1 to 6 on six faces, are thrown find the total number of possible outcomes ?


Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.


Find the number of ways in which one can post 5 letters in 7 letter boxes ?


Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?


In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes?


There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated ?


How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?


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


If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is


The number of words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate is


The number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, is


English alphabet has 11 symmetric letters that appear same when looked at in a mirror. These letters are A, H, I, M, O, T, U, V, W, X and Y. How many symmetric three letters passwords can be formed using these letters?


How many five digits telephone numbers can be constructed using the digits 0 to 9 If each number starts with 67 with no digit appears more than once?


In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?


Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.


Find the rank of the word ‘CHAT’ in the dictionary.


The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:


If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r


A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.

What is the maximum number of different answers can the students give?


In how many ways can the letters of the word SUCCESS be arranged so that all Ss are together?


Choose the correct alternative:
If Pr stands for rPr then the sum of the series 1 + P1 + 2P2 + 3P3 + · · · + nPn is


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 always together 


In how many ways 3 mathematics books, 4 history books, 3 chemistry books and 2 biology books can be arranged on a shelf so that all books of the same subjects are together.


In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?


The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.


The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.


In the permutations of n things, r taken together, the number of permutations in which m particular things occur together is `""^(n - m)"P"_(r - m) xx ""^r"P"_m`.


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

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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×