Advertisements
Advertisements
Question
3 boys and 3 girls are to sit in a row. How many ways can this be done if boys and girls are at alternate places
Solution
Since boys and girls are at alternate places, the 3 boys can occupy 3 odd places (Ist, 3rd, Sth) in 3P3 ways and 3 girls can occupy 3 even places (2nd, 4th, 6th) in 3P3, ways or the 3 boys can occupy 3 even places in 3P3, ways and 3 girls can occupy 3 odd places in 3P3, ways.
Hence, the total number of seating arrangements in which boys and girls are at alternate places.
= 3P3 × 3P3 + 3P3 × 3P3
= 3!3! + 3!3!
= 2 (3!)2
= 2(3 × 2 ×1)2
= 2 × 36
= 72
APPEARS IN
RELATED QUESTIONS
How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits are not allowed?
How many 4 letter words can be formed using letters in the word MADHURI if letters can be repeated?
Determine the number of arrangements of letters of the word ALGORITHM if vowels are always together.
Determine the number of arrangements of letters of the word ALGORITHM if consonants are at even positions.
Determine the number of arrangements of letters of the word ALGORITHM if O is the first and T is the last letter.
In a group photograph, 6 teachers are in the first row and 18 students are in the second row. There are 12 boys and 6 girls among the students. If the middle position is reserved for the principal and if no two girls are together, find the number of arrangements.
Find the number of ways letters of the word HISTORY can be arranged if Y and T are together.
Find the number of ways letters of the word HISTORY can be arranged if Y is next to T.
How many numbers can be formed using the digits 0, 1, 2, 3, 4, 5 without repetition so that the resulting numbers are between 100 and 1000?
Find the number of 6-digit numbers using the digits 3, 4, 5, 6, 7, 8 without repetition. How many of these numbers are not divisible by 5?
How many 4 letter words can be formed using letters in the word MADHURI if letters can be repeated
Determine the number of arrangements of letters of the word ALGORITHM if no two vowels are together.
Determine the number of arrangements of letters of the word ALGORITHM if consonants are at even positions.
Determine the number of arrangements of letters of the word ALGORITHM if O is the first and T is the last letter
Find the number of ways so that letters of the word HISTORY can be arranged as Y and T are together
Find the number of ways so that letters of the word HISTORY can be arranged as Y is next to T
Find the number of ways so that letters of the word HISTORY can be arranged as there is no restriction
Find the number of ways so that letters of the word HISTORY can be arranged as end in ST
Find the number of arrangements of the letters in the word SOLAPUR so that consonants and vowels are placed alternately
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 4, 5, 6, 8 if digits can be repeated
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 4, 5, 6, 8 if digits cannot be repeated
Find the number of 6-digit numbers using the digits 3, 4, 5, 6, 7, 8 without repetition. How many of these numbers are divisible by 5
In how many ways can 5 different books be arranged on a shelf if there are no restrictions
In how many ways can 5 different books be arranged on a shelf if 2 books are never together
3 boys and 3 girls are to sit in a row. How many ways can this be done if there are no restrictions
3 boys and 3 girls are to sit in a row. How many ways can this be done if there is a girl at each end
3 boys and 3 girls are to sit in a row. How many ways can this be done if all boys sit together
All the words that can be formed using alphabets A, H, L, U and R are written as in a dictionary (no alphabet is repeated). Rank of the word RAHUL is ______.
