There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.
Let us mark these positions as under:
(1) (2) (3) (4) (5) (6)
Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5.
Number of ways of arranging the vowels = = 3! = 6.
Also, the 3 consonants can be arranged at the remaining 3 positions.
Number of ways of these arrangements = = 3! = 6.
Total number of ways = (6 x 6) = 36.
DESIGN = 6 letters
No consonants appear at either of the two ends.
= = 2 x 4 x 3 x 2 x 1= 48
A Committee of 5 persons is to be formed from 6 gentlemen and 4 ladies by taking.
(i) 1 lady out of 4 and 4 gentlemen out of 6
(ii) 2 ladies out of 4 and 3 gentlemen out of 6
(iii) 3 ladies out of 4 and 2 gentlemen out of 6
(iv) 4 ladies out of 4 and 1 gentlemen out of 6
In case I the number of ways = = 4 x 15 = 60
In case II the number of ways = = 6 x 20 = 120
In case III the number of ways = = 4 x 15 = 60
In case IV the number of ways = = 1 x 6 = 6
Hence, the required number of ways = 60 + 120 + 60 + 6 = 246
The number of letters in the given word RITUAL = 6
Then,
Required number of different ways can the letters of the word 'RITUAL' be arranged = 6!
=> 6 x 5 x 4 x 3 x 2 x 1 = 720
Number of cards in a pack of cards = 52
Number of black cards = 26
Number of king cards = 4 (2 Red, 2 Black)
Required, the probability that if a card is drawn either card is black or a king =
Given total 16 Red roses and 14 White roses = 30 roses
Four flowers have to be selected from 30 i.e, = 27405 Ways
Now, atleast one Red rose is selected i.e, 27405(total) - 1(all four are white roses) = 27404 ways.
The first letter from the right can be chosen in 26 ways because there are 26 alphabets.
Having chosen this, the second letter can be chosen in 26 ways
The first two letters can chosen in 26 x 26 = 676 ways
Having chosen the first two letters, the third letter can be chosen in 26 ways.
All the three letters can be chosen in 676 x 26 =17576 ways.
It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
Each of the 10 letters can be posted in any of the 5 boxes.
So, the first letter has 5 options, so does the second letter and so on and so forth for all of the 10 letters.
i.e. 5*5*5*?.*5 (upto 10 times) = 5 ^ 10.
Given letters are k, l, m, n, o = 5
number of letters to be in the words = 3
Total number of words that can be formed from these 5 letters taken 3 at a time without repetation of letters =
15! - 14! - 13!
= (15 × 14 × 13!) - (14 × 13!) - (13!)
= 13! (15 × 14 - 14 - 1)
= 13! (15 × 14 - 15)
= 13! x 15 (14 - 1)
= 15 × 13 × 13!
Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that both marbles are blue = ³C?/¹?C? = (3 x 2)/(15 x 14) = 1/35
Probability that both are yellow = ²C?/¹?C? = (2 x 1)/(15 x 14) = 1/105
Probability that one blue and other is yellow = (³C? x ²C?)/¹?C? = (2 x 3 x 2)/(15 x 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35 = 3/35 + 1/105 = 1/35(3 + 1/3) = 10/(3 x 35) = 2/21
Comments
There are no comments.Copyright ©CuriousTab. All rights reserved.