Advertisements
Advertisements
Question
In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes?
Advertisements
Solution
(i) Since no student gets more than one prize; the first prize can be given to any one of the five students.
The second prize can be given to anyone of the remaining 4 students.Similarly, the third prize can be given to any one of the remaining 3 students.
The last prize can be given to any one of the remaining 2 students.
∴ Required number of ways =`5xx4xx3xx2=5!`
(ii) Since a student may get any number of prizes, the first prize can be given to any of the five students. Similarly, the rest of the three prizes can be given to the each of the remaining 4 students.
∴ Required number of ways =`5xx5xx5xx5=625`
(iii) None of the students gets all the prizes.
∴ Required number of ways = {Total ways of distributing the prizes in a condition wherein a student may get any number of prizes - Total ways in a condition in which a student receives all the prizes} =`625-5=620`
APPEARS IN
RELATED QUESTIONS
Compute `(8!)/(6! xx 2!)`
if `1/(6!) + 1/(7!) = x/(8!)`, find x
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?
Find n if n – 1P3 : nP4 = 1 : 9
Find r if `""^5P_r = 2^6 P_(r-1)`
Find r if `""^5P_r = ""^6P_(r-1)`
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
Evaluate each of the following:
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 ?
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 words that can be formed out of the letters of the word 'COMMITTEE' ?
The number of permutations of n different things taking r at a time when 3 particular things are to be included is
The number of five-digit telephone numbers having at least one of their digits repeated is
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
The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, 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?
How many six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?
Evaluate the following.
`(3! xx 0! + 0!)/(2!)`
The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:
The number of permutation of n different things taken r at a time, when the repetition is allowed is:
If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r
Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
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?
A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
How will the answer change if each question may have more than one correct answers?
How many strings can be formed from the letters of the word ARTICLE, so that vowels occupy the even places?
A coin is tossed 8 times, how many different sequences of heads and tails are possible?
A coin is tossed 8 times, how many different sequences containing six heads and two tails are possible?
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
In how many ways can 5 children be arranged in a line such that two particular children of them are never together.
Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated 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! |
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 ______.
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 ______.
The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
