Advertisements
Advertisements
Question
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
Options
12
24
18
none of these.
Advertisements
Solution
12
All S's can be placed either at even places or at odd places, i.e. in 2 ways.
The remaining letters can be placed at the remaining places in 3!, i.e. in 6 ways.
∴ Total number of ways = 6 x 2 = 12
APPEARS IN
RELATED QUESTIONS
Is 3! + 4! = 7!?
Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is 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?
Find n if n – 1P3 : nP4 = 1 : 9
Find r if `""^5P_r = ""^6P_(r-1)`
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there? How many possible outcomes if the coin is tossed four times? Five times? n times?
How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?
Evaluate each of the following:
6P6
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 all possible words that can be formed using the letters of the word 'MATHEMATICS'.
Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together ?
Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?
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 ways in which 6 men can be arranged in a row so that three particular men are consecutive, is
If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are
The number of ways in which the letters of the word ARTICLE can be arranged so that even places are always occupied by consonants 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?
If nP4 = 12(nP2), find n.
How many 6-digit telephone numbers can be constructed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each numbers starts with 35 and no digit appear more than once?
The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:
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:
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?
How many strings are there using the letters of the word INTERMEDIATE, if all the 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
DANGER
Choose the correct alternative:
The product of r consecutive positive integers is divisible b
Suppose m men and n women are to be seated in a row so that no two women sit together. If m > n, show that the number of ways in which they can be seated is `(m!(m + 1)!)/((m - n + 1)1)`
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 different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
| C1 | C2 |
| (a) 4 letters are used at a time | (i) 720 |
| (b) All letters are used at a time | (ii) 240 |
| (c) All letters are used but the first is a vowel | (iii) 360 |
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 ______.
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 ______.
