Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5
Find r if `""^5P_r = 2^6 P_(r-1)`
Find r if `""^5P_r = 2^6 P_(r-1)`
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?
How many 5-digit telephone numbers can be constructed using the digits 0 to 9. If each number starts with 67 and no digit appears more than once?
Find the number of ways in which one can post 5 letters in 7 letter boxes ?
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
In how many ways can 7 letters be posted in 4 letter boxes?
Evaluate each of the following:
Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2 ?
Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together ?
Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?
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 words from the letters of the word 'BHARAT' in which B and H will never come together, is
The number of arrangements of the word "DELHI" in which E precedes I 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
If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are
The number of arrangements of the letters of the word BHARAT taking 3 at a time is
The number of words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate is
If nP4 = 12(nP2), find n.
The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters 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?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if question number n has n + 1 choices?
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
Find the distinct permutations of the letters of the word MISSISSIPPI?
How many ways can the product a2 b3 c4 be expressed without exponents?
In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together
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 FUNNY are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, find the rank of the word FUNNY
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
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 ______.
Number of words from the letters of the words BHARAT in which B and H will never come together is ______.
