Advertisements
Advertisements
Question
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.
Advertisements
Solution
Given that P1, P2, P3, ... P10 are 10 persons out of which 5 persons are to be arranged but P1 must occur and P4 and P5 never occur
∴ Selection is to be done only for 10 – 3 = 7 persons
∴ Number of selection = 7C4
= `(7!)/(4!(7 - 4)!)`
= `(7!)/(4!3!)`
= `(7*6*5*4!)/(4!*3*2*1)`
= 35
5 people can be arranged as 5!
So, the number of arrangement = 35 × 5!
= 35 × 120
= 4200
Hence, the required arrangement = 4200.
APPEARS IN
RELATED QUESTIONS
Evaluate 4! – 3!
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?
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 r if `""^5P_r = 2^6 P_(r-1)`
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?
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.
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?
In how many ways can 5 different balls be distributed among three boxes?
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated ?
In how many ways can 4 letters be posted in 5 letter boxes?
Write the total number of possible outcomes in a throw of 3 dice in which at least one of the dice shows an even number.
Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?
The number of five-digit telephone numbers having at least one of their digits repeated is
The number of arrangements of the word "DELHI" in which E precedes I is
The number of ways to arrange the letters of the word CHEESE 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
How many six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
Evaluate the following.
`(3! xx 0! + 0!)/(2!)`
Evaluate the following.
`((3!)! xx 2!)/(5!)`
The number of permutation of n different things taken r at a time, when the repetition is allowed is ______.
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
A coin is tossed 8 times, how many different sequences containing six heads and two tails are possible?
How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative
How many strings are there using the letters of the word INTERMEDIATE, if vowels are never together
How many strings are there using the letters of the word INTERMEDIATE, if no two vowels are together
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?
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
If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?
A five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number of ways this can be done 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 ______.
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.
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 ______.
