Advertisements
Advertisements
Question
In how many ways can five children stand in a queue?
Solution
Required number of ways = Number of arrangements of all the children = 5P5 = 5!
We know:
nPn = n!
∴ 5P5 = 5! = 120
APPEARS IN
RELATED QUESTIONS
Convert the following products into factorials:
1 · 3 · 5 · 7 · 9 ... (2n − 1)
If (n + 1)! = 90 [(n − 1)!], find n.
Prove that:
If 5 P(4, n) = 6. P (5, n − 1), find n ?
If P(11, r) = P (12, r − 1) find r.
If P (n, 5) : P (n, 3) = 2 : 1, find n.
How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?
There are 6 items in column A and 6 items in column B. A student is asked to match each item in column A with an item in column B. How many possible, correct or incorrect, answers are there to this question?
In how many ways can 6 boys and 5 girls be arranged for a group photograph if the girls are to sit on chairs in a row and the boys are to stand in a row behind them?
In how many ways can the letters of the word 'FAILURE' be arranged so that the consonants may occupy only odd positions?
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels come together?
How many words can be formed out of the letters of the word, 'ORIENTAL', so that the vowels always occupy the odd places?
How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the letter G always occupies the first place?
How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the vowels always occupy even places?
How many permutations can be formed by the letters of the word, 'VOWELS', when
all consonants come together?
How many words can be formed out of the letters of the word 'ARTICLE', so that vowels occupy even places?
How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY, assuming that no letter is repeated, if all letters are used but first is vowel.
Find the number of words formed by permuting all the letters of the following words:
INDEPENDENCE
Find the number of words formed by permuting all the letters of the following words:
ARRANGE
Find the number of words formed by permuting all the letters of the following words:
PAKISTAN
Find the number of words formed by permuting all the letters of the following words:
EXERCISES
Find the number of words formed by permuting all the letters of the following words:
CONSTANTINOPLE
In how many ways can the letters of the word 'ALGEBRA' be arranged without changing the relative order of the vowels and consonants?
How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?
How many different signals can be made from 4 red, 2 white and 3 green flags by arranging all of them vertically on a flagstaff?
How many number of four digits can be formed with the digits 1, 3, 3, 0?
In how many ways can the letters of the word 'ARRANGE' be arranged so that the two R's are never together?
How many different arrangements can be made by using all the letters in the word 'MATHEMATICS'. How many of them begin with C? How many of them begin with T?
How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?
If the letters of the word 'LATE' be permuted and the words so formed be arranged as in a dictionary, find the rank of the word LATE.
In how many ways can the letters of the word
"INTERMEDIATE" be arranged so that:the vowels always occupy even places?
Prove that: 4nC2n : 2nCn = [1 · 3 · 5 ... (4n − 1)] : [1 · 3 · 5 ... (2n − 1)]2.
Write the expression nCr +1 + nCr − 1 + 2 × nCr in the simplest form.
Write the number of ways in which 5 red and 4 white balls can be drawn from a bag containing 10 red and 8 white balls.
Write the number of ways in which 12 boys may be divided into three groups of 4 boys each.