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# Permutation and Combination Questions

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How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?

A40

B400

C5040

D2520

Explanation:

LOGARITHMS' contains 10 different letters.

Required number of words = Number of arrangements of 10 letters, taking 4 at a time.
= 10P4
= (10 x 9 x 8 x 7)
= 5040.

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Consider the word ROTOR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5-letter palindromes?

A16576

B17576

C56689

D35142

Explanation:

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 be chosen in 26*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*26=17576 ways.
=> 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.

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How many different words can be formed using the letters of the word AMPLITUDE?

A9!

B9C6

C9P6

D9

Explanation:

AMPLITUDE:

All 9 letters are different so Number of words possible are 9!

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There are 5 Rock songs, 6 Carnatic songs and 3 Indi pop songs. How many different albums can be formed using the above repertoire if the albums should contain at least 1 Rock song and 1 Carnatic song?

A1500

B14624

C1500

D15624

Explanation:

Rock can be done in (2^5 - 1) = 32 - 1 = 31 ways.
6 Carnatic songs, choosing at least one, can be selected in 2^6 - 1 = 64 - 1 = 63 ways.
3 Indi pop can be selected in 2^3 = 8 ways

Therefore, the total number of combinations = 31 * 63 * 8 = 15624

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How many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears more than once?

A720

B360

C1420

D1680

Explanation:

6 digits telephone number can be formed by 10 digits (0,1,2...9)
So we have 8 digits remaining and 4 place.
So, 4 places can be formed in 8*7*6*5=1680.

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There are 20 balls which are red,blue,or green.If 7 balls are green and the sum of red balls and green balls is less than 13, at most how may red balls are ?

A5

B6

C7

D4

Explanation:

Green ball =7
G + R < 13
So, red can be 1 or 2 or 3 or 4 or 5
For atmost red ball take red = 5

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In a meeting between 2 countries each country has 12 delegates. All the delegates of one country shake hands with all delegates of other countries. Find the number of handshakes possible?

A72

B154

C144

DNone of these

Explanation:

Total no. of handshake = 12c1*12c1 = 144.

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In a cycle race there are 5 persons named as J,K,L,M,N participated for 5 positions. How many number of ways can M finishes always before N?

A55

B50

C60

D36

Explanation:

No. of ways in which 5 persons can finish is 5! = 120 (there are no ties)
Now, in half of these ways M can finish before N.

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There are 6561 balls out of them 1 is heavy. Find the min. no. of times the balls have to be weighed for finding out the heavy ball.

A12

B8

C18

D6

Explanation:

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In a dance school, there are 14 girls and 15 boys. In how many ways, a group consisting of 3 girls and 7 boys can be formed for a competition?

A2342340

B2232340

C2132840

D2132340

Explanation:

3 girls selected from 14 girls in 14C3 ways = 14! / 3! (14 - 3)! = 14! / 3!11! = 364 ways. (Formula used nCr = n! / r! (n-r)!)
And 7 boys selected from 15 boys in 15C7 ways = 15! / 7! (15 - 7)! = 15! / 7!8! = 6435 ways
So, possible ways = 364 x 6435 = 2342340 ways.

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