Advertisements
Advertisements
Question
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! |
Solution
| C1 | C2 |
| (a) Boys and girls alternate: | (i) (5!)2 + (5!)2 |
| (b) No two girls sit together : | (ii) 5! × 6! |
| (c) All the girls sit together | (iii) 2! 5! 5! |
| (d) All the girls are never together : | (iv) 10! – 5! 6! |
Explanation:
(a) Total number of arrangement when boys and girls alternate: = (5!)2 + (5!)2
(b) No two girls sit together: = 5! 6!
(c) All the girls sit together = 2! 5! 5!
(d) All the girls sit never together = 10! – 5! 6!
APPEARS IN
RELATED QUESTIONS
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:
A customer forgets a four-digits code for an Automatic Teller Machine (ATM) in a bank. However, he remembers that this code consists of digits 3, 5, 6 and 9. Find the largest possible number of trials necessary to obtain the correct code.
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?
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.
Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?
In how many ways can 5 different balls be distributed among three boxes?
In how many ways can 7 letters be posted in 4 letter boxes?
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 ?
In how many ways 4 women draw water from 4 taps, if no tap remains unused?
Write the number of words that can be formed out of the letters of the word 'COMMITTEE' ?
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
If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are
Find x if `1/(6!) + 1/(7!) = x/(8!)`
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?
Find the rank of the word ‘CHAT’ in the dictionary.
Evaluate the following.
`(3! + 1!)/(2^2!)`
If `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
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?
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
If the letters of the word FUNNY are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, find the rank of the word FUNNY
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
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
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.
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
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.
