Advertisements
Advertisements
प्रश्न
Four letters E, K, S and V, one in each, were purchased from a plastic warehouse. How many ordered pairs of letters, to be used as initials, can be formed from them?
उत्तर
Here, we need to find out the number of pairs of the letters that can be formed with the 4 letters.
Required number of ordered pairs = Number of arrangements of four letters, taken two at a time = 4P2
\[= \frac{4!}{\left( 4 - 2 \right)!}\]
\[ = \frac{4!}{2!}\]
\[ = \frac{4 \times 3 \times 2!}{2!}\]
\[ = 4 \times 3\]
\[ = 12\]
APPEARS IN
संबंधित प्रश्न
Convert the following products into factorials:
(n + 1) (n + 2) (n + 3) ... (2n)
If (n + 1)! = 90 [(n − 1)!], find n.
Prove that:
Prove that:
\[\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!} = \frac{(n + 1)!}{r! (n - r + 1)!}\]
Prove that:
If nP4 = 360, find the value of n.
If P (n − 1, 3) : P (n, 4) = 1 : 9, find n.
How many three-digit numbers are there, with distinct digits, with each digit odd?
How many words, with or without meaning, can be formed by using all the letters of the word 'DELHI', using each letter exactly once?
How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?
How many 6-digit telephone numbers can be constructed with digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each number starts with 35 and no digit appears more than once?
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?
If a denotes the number of permutations of (x + 2) things taken all at a time, b the number of permutations of x things taken 11 at a time and c the number of permutations of x − 11 things taken all at a time such that a = 182 bc, find the value of x.
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels occupy only the odd places?
How many words can be formed from the letters of the word 'SUNDAY'? How many of these begin with D?
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 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 4 letters are used at a time?
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:
PAKISTAN
Find the number of words formed by permuting all the letters of the following words:
EXERCISES
How many number of four digits can be formed with the digits 1, 3, 3, 0?
Find the number of numbers, greater than a million, that can be formed with the digits 2, 3, 0, 3, 4, 2, 3.
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?
Prove that the product of 2n consecutive negative integers is divisible by (2n)!
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
n · n − 1Cr − 1 = (n − r + 1) nCr − 1
How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if all letters are used but first letter is a vowel?
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
If 35Cn +7 = 35C4n − 2 , then write the values of n.
Write the number of diagonals of an n-sided polygon.
Write the total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants.
