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
Evaluate 8!
if `1/(6!) + 1/(7!) = x/(8!)`, find x
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?
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?
In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
Find x in each of the following:
Find x in each of the following:
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?
Evaluate each of the following:
P(6, 4)
Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2 ?
The number of ways in which the letters of the word 'CONSTANT' can be arranged without changing the relative positions of the vowels and consonants is
The number of ways to arrange the letters of the word CHEESE are
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
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
Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
If `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n
How many ways can the product a2 b3 c4 be expressed without exponents?
A coin is tossed 8 times, how many different sequences of heads and tails are possible?
How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative
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?
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 of these 6-digit numbers are even?
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 of these 6-digit numbers are divisible by 4?
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
Choose the correct alternative:
If `""^(("n" + 5))"P"_(("n" + 1)) = ((11("n" - 1))/2)^(("n" + 3))"P"_"n"`, then the value of n are
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
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)`
The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.
The total number of 9 digit numbers which have all different digits is ______.
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! |
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.
