Arithmetic Aptitude :: Permutation and Combination

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In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?


A63

B90

C126

D45

E135

Answer: Option A

Explanation:

Total 7 men and 3 women



5 men can be selected from 7 men in 7C5 ways



2 women can be selected from 3 women in 3C2 ways



So 7C5*3C2= 63 ways.

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In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?


A810

B1440

C2880

D50400

Answer: Option D

Explanation:

In the word "CORPORATION",treat those vowels OOAIO as one letter.

so it will be "CRPRTN (OOAIO)".

which is having 7 (6 + 1) letters. out of which R occurs 2 times and the rest are different.

Number of ways arranging these letters = (7!/2!) = 2520.


Now 5 vowels in which O occurs 3 times and the rest are different, can be arranged as 5!/3! = 20 ways.

So required number of ways = (2520 x 20) = 50400.

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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

Answer: Option C

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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23 people are there, they are shaking hands together, how many hand shakes possible, if they are in pair of cyclic sequence.


A23

B20

C22

D1

ENone of these

Answer: Option C

Explanation:

23-people-are-there-they-are-shaking-hands-together

 

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Six friends go to pizza corner there are 2 types of pizzas. And six different flavors are there they have to select 2 flavors from 6 flavors. In how many ways we can select?


A6C2

B6P2

C(6C2)/2!

DNone of these

Answer: Option A

Explanation:

Number of ways 2 flavors can be selected out of 6 flavors = 6c2 = 15

Number of ways pizza can be selected = 2 [there are 2 types of pizzas]

∴ Number of ways to select a pizza = 2 × 15 = 30 ways

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36 people {a1, a2, ..., a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is


A12

B11

C13

D18

Answer: Option D

Explanation:

meet-and-shake-hands-in-a-circular-fashion

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From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?


A564

B645

C735

D756

Answer: Option D

Explanation:

We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).

Required number of ways = (7C3 * 6C2)+(7C4 * 6C1)+(7C5)
=>[(7*6*5)/(3*2*1) * (6*5)/(2*1)]+(7C3 * 6C1) + (7C2)

=> 525 + [(7*6*5)/(3*2*1)* 6]+[(7*6)/(2*1)]

= (525 + 210 + 21)
= 756

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In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?


A10080

B4989600

C120960

DNone of these

Answer: Option C

Explanation:

In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.
Thus, we have MTHMTCS (AEAI).
Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.

So,Number of ways of arranging these letters = (8!/2!*2!)=10080.

Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.

Number of ways of arranging these letters = (4!/2)=12.
=> Required number of words = (10080 * 12) = 120960.

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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

Answer: Option B

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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In how many ways can an animal trainer arrange 5 lions and 4 tigers in a row so that no two lions are together


A2880

B1440

C5760

DNone of these

Answer: Option A

Explanation:

The lions and the tigers can be arranged in 5!*4!= 2880 ways

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