Advertisements
Advertisements
प्रश्न
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?
उत्तर
There are six letters in the word MONDAY.
All the letters are used, but the first letter is a vowel:
There are two vowels, namely A and O, in the word MONDAY.
For the first letter, out of the two vowels, one vowel can be chosen in 2C1 ways.
The remaining five letters can be chosen in 5C5 ways.
So, the letters in 5C5 group can be arranged in \[5!\]ways.
∴ Number of ways =\[{}^2 C_1 \times^5 C_5 \times 5! = 2 \times 1 \times 5! = 240\]
APPEARS IN
संबंधित प्रश्न
Convert the following products into factorials:
5 · 6 · 7 · 8 · 9 · 10
Convert the following products into factorials:
3 · 6 · 9 · 12 · 15 · 18
Convert the following products into factorials:
(n + 1) (n + 2) (n + 3) ... (2n)
If (n + 1)! = 90 [(n − 1)!], find n.
If P (5, r) = P (6, r − 1), find r ?
If P (n, 5) = 20. P(n, 3), find n ?
If P (9, r) = 3024, find r.
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?
There are two works each of 3 volumes and two works each of 2 volumes; In how many ways can the 10 books be placed on a shelf so that the volumes of the same work are not separated?
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 come together?
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 letters P and I respectively occupy first and last place?
m men and n women are to be seated in a row so that no two women sit together. if m > n then show that the number of ways in which they can be seated as\[\frac{m! (m + 1)!}{(m - n + 1) !}\]
How many three letter words can be made using the letters of the word 'ORIENTAL'?
Find the number of words formed by permuting all the letters of the following words:
INDIA
Find the number of words formed by permuting all the letters of the following words:
RUSSIA
Find the number of words formed by permuting all the letters of the following words:
EXERCISES
In how many ways can the letters of the word 'ALGEBRA' be arranged without changing the relative order of the vowels and consonants?
Find the total number of arrangements of the letters in the expression a3 b2 c4 when written at full length.
How many words can be formed with the letters of the word 'PARALLEL' so that all L's do not come together?
There are three copies each of 4 different books. In how many ways can they be arranged in a shelf?
A biologist studying the genetic code is interested to know the number of possible arrangements of 12 molecules in a chain. The chain contains 4 different molecules represented by the initials A (for Adenine), C (for Cytosine), G (for Guanine) and T (for Thymine) and 3 molecules of each kind. How many different such arrangements are possible?
How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?
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.
If the letters of the word 'MOTHER' are written in all possible orders and these words are written out as in a dictionary, find the rank of the word 'MOTHER'.
In how many ways can the letters of the word
"INTERMEDIATE" be arranged so that:the vowels always occupy even places?
Prove that the product of 2n consecutive negative integers is divisible by (2n)!
Evaluate
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
nCr + 2 · nCr − 1 + nCr − 2 = n + 2Cr.
There are 10 persons named\[P_1 , P_2 , P_3 , . . . . , P_{10}\]
Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
If 35Cn +7 = 35C4n − 2 , then write the values of n.
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.
