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Permutation and Combination Questions

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31 / 100

Choose the correct option.

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

Answer: Option A

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.

Workspace

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SHSTTON
10
Solv. Corr.
35
Solv. In. Corr.
45
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Avg. Time

32 / 100

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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

Answer: Option D

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.

Workspace

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SHSTTON
35
Solv. Corr.
11
Solv. In. Corr.
46
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33 / 100

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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

Answer: Option D

Explanation:

DELHI



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

Workspace

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SHSTTON
25
Solv. Corr.
32
Solv. In. Corr.
57
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34 / 100

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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

Answer: Option C

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

NA
SHSTTON
46
Solv. Corr.
76
Solv. In. Corr.
122
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0 M:20 S
Avg. Time

35 / 100

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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

Answer: Option A

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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SHSTTON
10
Solv. Corr.
41
Solv. In. Corr.
51
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36 / 100

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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

Answer: Option A

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

Workspace

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17
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36
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37 / 100

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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

Answer: Option D

Explanation:

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

Workspace

NA
SHSTTON
12
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28
Solv. In. Corr.
40
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38 / 100

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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

Answer: Option C

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

NA
SHSTTON
42
Solv. Corr.
102
Solv. In. Corr.
144
Attempted
1 M:42 S
Avg. Time

39 / 100

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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

Answer: Option D

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

NA
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43
Solv. Corr.
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102
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40 / 100

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


A570

B526

C576

DNone of these

Answer: Option C

Explanation:

6!-4!*3!=576

Workspace

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