Advertisements
Advertisements
Question
The number of ways to arrange the letters of the word CHEESE are
Options
120
240
720
6
Advertisements
Solution
120
Total number of arrangements of the letters of the word CHEESE = Number of arrangements of 6 things taken all at a time, of which 3 are of one kind =\[\frac{6!}{3!}\]= 120
APPEARS IN
RELATED QUESTIONS
if `1/(6!) + 1/(7!) = x/(8!)`, find x
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
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?
Find x in each of the following:
Find x in each of the following:
If three six faced die each marked with numbers 1 to 6 on six faces, are thrown find the total number of possible outcomes ?
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?
Evaluate each of the following:
8P3
Evaluate each of the following:
In how many ways can 4 letters be posted in 5 letter boxes?
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 ?
The number of arrangements of the letters of the word BHARAT taking 3 at a time is
If (n+2)! = 60[(n–1)!], find n
How many numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?
If nP4 = 12(nP2), find n.
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
The possible outcomes when a coin is tossed five times:
If n is a positive integer, then the number of terms in the expansion of (x + a)n is:
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
8 women and 6 men are standing in a line. In how many arrangements will all 6 men be standing next to one another?
8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?
How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative
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
Choose the correct alternative:
If `""^(("n" + 5))"P"_(("n" + 1)) = ((11("n" - 1))/2)^(("n" + 3))"P"_"n"`, then the value of n are
In how many ways can 5 children be arranged in a line such that two particular children of them are always together
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur 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?
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! |
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 ______.
If m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.
