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# Permutation and Combination Questions

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31 / 100

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When all possible six-letter arrangements of the letters of the word "MASTER" are sorted in alphabetical order, what will be the 49th word?

AAREMST

BARMEST

CAMERST

DARMSET

Explanation:

Arrange "MASTER" as AEMSTR
AE _ _ _ _,this is for "MSTR",will be arranged as 4!=24.
AM _ _ _ _,this is for "ESTR",will be arranged as 4!=24.
so total words = 48.
now 49th word will be start from AR and will be AREMST.

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Oranges can be packed in sets of 10 oranges in box type A or 25 oranges in box type B. A carton comprising of 1000 oranges of type a and b is packed. How many different combinations are possible in the number of type A and type B boxes while organizing the oranges?

A18

B19

C20

D21

Explanation:

25x+10y=1000
Find all posiible value of (x,y)
for satisfying eqtn "b" must be even & the range of "b" will varry from 0 to 40. so total no. is 21 ways.

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How many words with or without meaning, can be formed by using all the letters of the word, DELHI using each letter exactly once?

A720

B24

C23

D120

Explanation:

DELHI

All 5 letters are different so Number of words possible are: 5!= 120

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For the word SURITI, if you arrange the letters in dictionary order then what is its rank?

A234

B235

C236

D237

Explanation:

I= 5! =120
R=5!/2 =60
SI=4! =24
SR=4!/2= 12
ST=4!/2= 12
SUI=3! = 6
= 234 WORDS

and the below 2 words as
SURIIT
SURITI
234 + 2 = 236
So, rank = 236

Workspace

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Mr verma has 4 different paintings that he wishes to divide among his 3 children. In how many ways can he do this if each child must get at least 1 painting and all paintings are different ?

A72

B46

C36

D34

Explanation:

First child could get 1 out of 4 paintings: 4
Second can get 1 out of remaining 3: 3
Third will get 1 out of remaining 2: 2
Now the last painting could be given to any of the three child in 3 diff ways:
Thus, total number of ways: (4 * 3 * 2) * 3 = 72.

Workspace

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How many 5 digit numbers can be formed which are divisible by 3 using the numerals 0, 1, 2, 3, 4, 5 (WITHOUT REPETITION)

A216

B315

C240

D600

Explanation:

As per the question the five digit number should be divisible by 3.
So, only possible 5 digit numbers are{1,2,3,4,5} => sum is 15 and {0,1,2,4,5} sum=>12
{1, 2, 3, 4, 5} --> 5! =120
and for {0,1,2,4,5}
"0" can not be used at first place as number will be 4 digit.
So,Total numer = (5!-4!) = 96
120+96=216

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A father of 6 children takes 2 of his children at a time to a circus as often as he can, without taking the same pair of children together more than once. How many times does the father go tothe circus?

A11

B8

C13

D15

ENone of these

Explanation:

He has to choose 2 children from 6
total number of combinations=6c2=15
Father goes to circus 15 times

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8 chairs are numbered from 1 to 8. Two women first choose two chairs from those marked 1 to 4 and 3 men selects 3 chairs from the remaining. Find the number of possible arrangements

A124

B120

C1440

DNone of these

Explanation:

2 women choose 2 chairs from 4 in 4P2 ways.
reamining 6, 3 men selects 3 chairs in 6p3 ways

So, Total arrangements=12*120=1440

Workspace

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How many words can be formed using the letters of the word "CORRESPONDANCE" if the consonants are always written together?

A182

B184

C216*9!

DNone of these

Explanation:

Acc. to the question, the word can be split up into two halves , (CRRSPNDNC) & (OEOAE)
Now these two can be arranged among themselves in 2! Ways.
Now (CRRSPNDNC) can be arranged in 9!/(2!*2!*2!) ways
Similarly (OEOAE) can be done in 6!/(2!*2!) ways.
When all 3 cases put together= 2!* 9!/(2!*2!*2!)* 6!/(2!*2!)= 45*9!

Workspace

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How many ways word "ORANGE" can be arranged, In which vowels are not together

A570

B526

C576

DNone of these

Explanation:

6!-4!*3!=576

Workspace

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