Advertisements
Advertisements
प्रश्न
Find the distinct permutations of the letters of the word MISSISSIPPI?
Advertisements
उत्तर
The given word is MISSISSIPPI.
Number of letters in the word = 11
Number of S’s = 4
Number of I’s = 4
Number of P’s = 2
Number of M’s = I
Hence the total number of distinct words
= `(11!)/(4! xx 4! xx 2! xx 1!)`
= `(11 xx 10 xx 9 xx 8 xx 7 xx 6 xx 5 xx 4!)/(4 xx 3 xx 2 xx 1 xx 4! xx 2 xx 1 xx 1)`
= `(11 xx 10 xx 9 xx 8 xx 7 xx 6 xx 5)/(4 xx 3 xx 2 xx 2)`
= `(11 xx 10 xx 9 xx 8 xx 7 xx 6 xx 5)/(8 xx 6)`
= 10 × 10 × 9 × 7 × 5
= 34,650
APPEARS IN
संबंधित प्रश्न
Evaluate 8!
Compute `(8!)/(6! xx 2!)`
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
Find r if `""^5P_r = 2^6 P_(r-1)`
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?
Evaluate each of the following:
8P3
The number of different signals which can be given from 6 flags of different colours taking one or more at a time, is
The number of arrangements of the word "DELHI" in which E precedes I is
How many six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?
If (n+2)! = 60[(n–1)!], find n
Find the rank of the word ‘CHAT’ in the dictionary.
Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?
8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many distinct 6-digit numbers are there?
Choose the correct alternative:
If Pr stands for rPr then the sum of the series 1 + P1 + 2P2 + 3P3 + · · · + nPn is
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.
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.
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! |
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 ______.
