Permutations & Combinations
Important Instructions
In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
Answer: C
The word 'LEADING' has 7 different letters.
When the vowels EAI are always together, they can be supposed to form one letter.
Then, we have to arrange the letters LNDG (EAI).
Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.
The vowels (EAI) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
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A box contains 2 white, 3 black and 5 red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?
Answer: D
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In how many different ways can six players be arranged in a line such that two of them, Ajeet and Mukherjee are never together?
Answer: D
As there are six players, So total ways in which they can be arranged = 6!ways =720.
A number of ways in which Ajeet and Mukherjee are together = 5!x2 = 240.
Therefore, Number of ways when they don’t remain together = 720 -240 =480.
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In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
Answer: D
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The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is -.
Answer: C
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How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}
Answer: D
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A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?
Answer: A
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A mixed doubles tennis game is to be played two teams(each consists of one male and one female) There are four married couples. No team is to consist a husband and his wife. What is the maximum number of games that can be played?
Answer: D
Married couples = MF MF MF MF
AB CD EF GH
Possible teams = AD CB EB GB
AF CF ED GD
AH CH EH GF S
Since one male can be paired with 3 other female, Total teams = 4x3 = 12.
Team AD can play only with CB,CF,CH,EB,EH,GB,GF(7 teams )
Team AD cannot play with AF, AH, ED and GD
The same will apply with all teams, So number of total matches = 12x7 = 84.
But every match includes 2 teams, so the actual number of matches = 84/2 = 42.
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2 men and 1 woman board a bus of which 5 seats are vacant, one of these 5 seats is reserved for ladies. A woman may or may not sit on the seat reserved for ladies, In how many different ways can the five seats be occupied by these passengers?
Answer: B
Case I if lady sits on the reserved seat, then 2 men can occupy seats from 4 vacant seats in = 4P2 = 4x3 = 12ways
Case II if lady does not sit on reversed seat, then I. Woman can occupy a seat from four seats in 4 ways. I. man can occupy a seat from 3 seats in 3 ways, also I. man left can occupy a seat from remaining two seats in 2 ways.
Therefore, Total ways = 4x3x2 = 24ways
From case I and case II
Total number of ways = 12+24 = 36
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What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?
Answer: C
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Topics
- Number System
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