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The number of ways in which five vowels of English alphabets and ten decimal digits can be placed in a row such that between any two vowels, odd number of digits are placed and both end places are occupied by vowels, is $20 (b!) (5!)$ . Then evaluate $b$ .

Important Questions on Permutation and Combination

HARD

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 26

The number of integers which lie between

1

and

10^{6}

and which have the sum of the digits equal to

12

N

then

b = 10 .

is equal to

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 27

The number of ways in which

8

non-identical apples can be distributed among

3

boys such that every boy should get atleast

1

apple & atmost

4

apples is

N

then

(\frac{N}{60})

is equal to

EASY

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 28

in a hockey series between team

X

and

Y,

they decide to play till a team wins

' 10'

match. Then the number of ways in which a team

X

wins is

\frac{{}^{20}C_{m}}{2}

then

m

is equal to

HARD

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 29

Three ladies have brought one child each for admission to a school. The principal wants to interview the six persons one by one subject to the condition that no mother is interviewed before her child. Then find the number of ways in which interviews can be arranged.

EASY

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 30

In a shooting competition, a man can score

0, 2

4

points for each shot. Then the number of different ways in which he can score

14

points in

5

shots is

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 31

Six persons

A, B, C, D, E

and

F

are to be seated at a circular table. The number of ways this can be done if

A

must have either

B

C

on his right and

B

must have either

C

D

on his right is

EASY

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 32

The number of permutations which can be formed out of the letters of the word

" SERIES "

taking three letters together is

HARD

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 33

A box contains

6

balls which may be all of different colours or three each of two colours or two each of three different colours. The number of ways of selecting

3

balls from the box (if ball of same colour are identical) is

The number of ways in which five vowels of English alphabets and ten decimal digits can be placed in a row such that between any two vowels, odd number of digits are placed and both end places are occupied by vowels, is 20b!5!. Then evaluate b.

Important Questions on Permutation and Combination

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The number of ways in which five vowels of English alphabets and ten decimal digits can be placed in a row such that between any two vowels, odd number of digits are placed and both end places are occupied by vowels, is $20 (b!) (5!)$ . Then evaluate $b$ .