Advertisements
Advertisements
प्रश्न
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?
Advertisements
उत्तर
In the given word MISSISSIPPI, I appears 4 times, S appears 4 times, P appears 2 times, and M appears just once.
Therefore, number of distinct permutations of the letters in the given word
= `(11!)/(4!4!2!)`
= `(11 xx 10 xx 9 xx 8 xx 7 xx 6 xx 5 xx 4!)/(4! xx 4 xx 3 xx 2 xx 1 xx 2 xx 1)`
= `(11 xx 10 xx 9 xx 8 xx 7 xx 6 xx 5)/(4 xx 3 xx 2 xx 1xx 2 xx 1)`
= 34650
There are 4 Is in the given word. When they occur together, they are treated as a single object 
for the time being. This single object, together with the remaining 7 objects, will account for 8 objects.
These 8 objects, in which there are 4 Ss and 2 Ps, can be arranged in `(8!)/(4!2!)` ways, i.e.,
840 ways.
Number of arrangements where all Is occur together = 840
Thus, number of distinct permutations of the letters in MISSISSIPPI in which four Is do not come together = 34650 – 840 = 33810
APPEARS IN
संबंधित प्रश्न
Evaluate 4! – 3!
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?
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?
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 vowels are all together.
How many 5-digit telephone numbers can be constructed using the digits 0 to 9. If each number starts with 67 and no digit appears more than once?
Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.
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 ?
Evaluate each of the following:
Write the number of ways in which 7 men and 7 women can sit on a round table such that no two women sit together ?
Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together ?
The number of six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters is
A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is
If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are
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
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 six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear 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?
Evaluate the following.
`((3!)! xx 2!)/(5!)`
If n is a positive integer, then the number of terms in the expansion of (x + a)n is:
The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:
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
Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
8 women and 6 men are standing in a line. In how many arrangements will all 6 men be standing next to one another?
In how many ways can the letters of the word SUCCESS be arranged so that all Ss are together?
How many strings are there using the letters of the word INTERMEDIATE, if vowels are never together
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is ______.
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
There are 10 persons named P1, P2, P3, ... P10. 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.
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 permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ______.
