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
Evaluate 8!
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)`
Find x in each of the following:
Which of the following are true:
(2 +3)! = 2! + 3!
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 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?
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?
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?
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 ?
Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2 ?
The number of different signals which can be given from 6 flags of different colours taking one or more at a time, is
A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done 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 (n+2)! = 60[(n–1)!], find n
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
- In how many ways can 8 identical beads be strung on a necklace?
- In how many ways can 8 boys form a ring?
Evaluate the following.
`(3! + 1!)/(2^2!)`
Find the distinct permutations of the letters of the word MISSISSIPPI?
In how many ways can the letters of the word SUCCESS be arranged so that all Ss 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
Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85th string?
Choose the correct alternative:
If `""^(("n" + 5))"P"_(("n" + 1)) = ((11("n" - 1))/2)^(("n" + 3))"P"_"n"`, then the value of n are
Choose the correct alternative:
The product of r consecutive positive integers is divisible b
In how many ways can 5 children be arranged in a line such that two particular children of them are always together
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
The total number of 9 digit numbers which have all different digits 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 ______.
In the permutations of n things, r taken together, the number of permutations in which m particular things occur together is `""^(n - m)"P"_(r - m) xx ""^r"P"_m`.
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 |
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 ______.
Number of words from the letters of the words BHARAT in which B and H will never come together is ______.
