|nPr = n(n – 1)(n – 2) … (n – r + 1) =||n!|
|(n – r)!|
|Then, number of permutations of these n objects is =||n!|
|nCr =||n!||=||n(n – 1)(n – 2) … to r factors||.|
|(r!)(n – r)!||r!|
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How many numbers of 3-digits can be formed with the digits 1, 2, 3, 4, 5
(repetition of digits not allowed )?
In how many ways can 5 prices distributed to 8 students if each student can get any number of prizes?
How many straight lines can be formed from 8 non-collinear points on the X-Y plane?
In how many ways can the letters of the word PATNA be rearranged?
In question no. 4, how many words will start with P and end with T?
How many numbers of 4 digits can be formed with the digits 0, 1, 2, 3 (repetition of digits is not allowed)?
How many numbers between 200 and 1200 can be formed with the digits 0,1,2,3 (repetition of digit is not allowed)?
How many four digit numbers are possible, criteria being that all the four digits are odd?
In how many ways can ram choose a vowel and a consonant from the letters of the word ALLAHABAD?
How many new words are possible from the letters of the word PERMUTATION?
In how many ways can 12 papers be arranged if the best and the worst paper never come together?
How many 7-digit numbers are there having the digit 3 three times and the digit 0 four times?
In how many ways a selection can be made of at least one fruit out of the 5 bananas, 4 mangoes and 4 almonds?
How many numbers can be formed with the digits 1,6,7,8,6,1 so that the odd digits always occupy the odd places?
How many rounds of matches does a knock-out tennis tournament have if it starts with 64 players and every player needs to win 1 match to move at the next ground?
There are nine points in a plane such that exactly three points out of them are collinear. Find the number of triangles that can be formed using these points as vertices.
How many numbers greater than 0 and less than a million can be formed with digits 0,7 and 8?
How many even numbers of four digits can be formed with the digits 1, 2, 3, 4, 5, 6 (repetitions of digits are allowed )?
How many 4 digit numbers divisible by 5 can be formed with the digits 0,1,2,3,4,5,6 and 6?
There are 6 pups and 4 cats. In how many ways can they be seated in a row so that no cat sit together?
How many new words can be formed with the word MANAGEMENT all ending in G?
Find the total no. of 9-digit numbers thst can be formed all having different digits ?
In how many ways 5 MBA students and six law students can be arranged together so that no two MBA student are side by side?
Find the sum of the numbers of sides and no. of diagonals of a hexagon?
In how many ways can a selection be made of 5 letters out of 5As, 4Bs, 3Cs, 2Dsand 1E?
The no. of positive numbers of not more than 10 digits formed by using 0,1,2,3 is
There is a no. lock with four rings. How many attempts at the maximum would have to be made before getting the right no.?
If a team of four persons is to be selected from 8 males and 8 females, then in how many ways can the selections be made to include at least one male .
In the above question, in how many ways can the selections we made if it has to contain had the maximum three women?
How many figures are required to number a book containing 150 pages?
There are 8 orators A, B,C,D,E,F,G and H. in how many ways can the arrangements we made so that A always comes before B and B always comes before C.
There are four letters and 4 envelops. In how many ways can wrong choices be made?
In the question above, find the no. of ways in which only one letter goes in the wrong envelop?
In question 15, find the no. of ways in which only two letters go in the wrong envelop?
How many 6-digit numbers have all their digits either all odd or all even?
How many 6 digit numbers have at least 1 even digit?
How many 10 digit numbers have at least 2 equal digit?
The number of circle that can be drawn out of 10 points of which 7 are collinear is
How many different 9-digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions?
A polygon has 54 diagonals. Find the number of sides.
The number of natural number of two or more than two digits from left to right are in increasing order is
In how many ways the cricketer can spoke 200 runs with fours and sixes only?
A dices is rolled six times. One, two, three, four, five and six appers on consecutive throws of dices. How many ways are possible of having 1 before 6?
The number of permutations of the letters a, b, c, d, e, f, g such that neither the pattern ‘beg’ nor ‘acd’ occurs is
In how many ways can the letters of the English alphabet be arranged so that there are seven letters between the letters a and b?
How many rectangles can be formed out of a chessboard?
Seven different objects must be divided among three people. In how many ways can this be done if at least one of them gets exactly 1 object?
How many 4–digit numbers that are divisible by 4 can be formed from the digits 1,2,3,4 and 5?
How many natural numbers smaller than 10000 are there in the decimal notation of which all the digits are different?
How many 4-digit numbers are there whose decimal notation contains not more than two distinct digits?
How many different 7-digit numbers are there the sum of whose digits are odd?
How many 6-digit numbers contain exactly 4 different digits?
How many different numbers which are smaller that 2.10⁸ can be formed using the digits 1 and 2 only?
How many distinct 6-digit numbers are there having 3 odd and 3 even digits?
How many 8-digit numbers are there the sum of whose digits is even?
How many natural numbers not more than 4300 can be formed with the digits 0,1,2,3,4 (if repetitions are allowed)?
How many natural numbers less than 4300 can be formed with the digits 0,1,2,3,4 ( if repetitions are not allowed)?