Advertisements
Advertisements
प्रश्न
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 ?
Advertisements
उत्तर
B_B_B_B_B
Five boys can be arranged amongst themselves in 5! ways, at the places shown above.
The three girls are now to be arranged in the remaining four places taken three at a time = 4P3 = 4!
By fundamental principle of counting, total number of ways = 5! x 4! = 120 x 24= 2880
APPEARS IN
संबंधित प्रश्न
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
Find r if `""^5P_r = 2^6 P_(r-1)`
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.
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?
Evaluate each of the following:
8P3
Evaluate each of the following:
Evaluate each of the following:
6P6
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 arrangements of the letters of the word BANANA in which two N's come together.
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 all possible words that can be formed using the letters of the word 'MATHEMATICS'.
The number of words from the letters of the word 'BHARAT' in which B and H will never come together, is
The product of r consecutive positive integers is divisible by
If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are
How many numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?
If nP4 = 12(nP2), find n.
Find the rank of the word ‘CHAT’ in the dictionary.
Evaluate the following.
`(3! + 1!)/(2^2!)`
If n is a positive integer, then the number of terms in the expansion of (x + a)n is:
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
The number of permutation of n different things taken r at a time, when the repetition is allowed is ______.
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
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?
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?
How many ways can the product a2 b3 c4 be expressed without exponents?
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?
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
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
Choose the correct alternative:
If Pr stands for rPr then the sum of the series 1 + P1 + 2P2 + 3P3 + · · · + nPn is
How many words can be formed with the letters of the word MANAGEMENT by rearranging them?
In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
Using the digits 1, 2, 3, 4, 5, 6, 7, a number of 4 different digits is formed. Find
| C1 | C2 |
| (a) How many numbers are formed? | (i) 840 |
| (b) How many number are exactly divisible by 2? | (i) 200 |
| (c) How many numbers are exactly divisible by 25? | (iii) 360 |
| (d) How many of these are exactly divisible by 4? | (iv) 40 |
If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ______.
