The number of three digit numbers of the form x y z such that x < y and z ≤ y is N then N - 225 is equal to

Let y = n ⇒ x ∈ 1 , 2 , . . . n - 1 and z ∈ 0 , 1 , 2 , . . . n as x ≠ 0 , so the number of possible values of x = n - 1 and the number of possible values of z = n + 1 As we know, for y , n ∈ 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 So, the number of three-digit numbers N = ∑ 2 9 n - 1 n + 1 = ∑ 2 9 n 2 - 1 = ∑ 2 9 n 2 - ∑ 2 9 1 = n n + 1 2 n + 1 6 - 9 = 9 × 10 × 19 6 - 9 = 276 So, N - 225 = 51 .

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IMPORTANT

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Let $P_{n}$ denotes the number of ways of selecting $3$ people out of $' n'$ sitting in a row if no two of them are consecutive and $Q_{n}$ is the corresponding figure when they are in a circle. If $P_{n} - Q_{n} = 6,$ then $' n'$ is equal to

Important Questions on Permutation and Combination

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 39

The number of ways selecting

8

books from a library which has

10

books each of Mathematics, Physics, Chemistry and English, if books of the same subject are alike, is

(N^{2} - 4)

then

N

is equal to

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 40

The number of three digit numbers of the form

x y z

such that

x < y

and

z \leq y

N

then

(N - 225)

is equal to

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 41

In an examination, a candidate is required to pass in all the four subjects he is studying. The number of ways in which he can fail is

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 42

The kindergarten teacher has

25

kids in her class. She takes

5

of them at a time, to zoological garden as often as she can, without taking the same

5

kids more than once. Then the number of visits, the teacher makes to the garden exceeds that of a kid by:

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 43

A student has to answer

10

out of

13

questions in an examination. The number of ways in which he can answer if he must answer atleast

3

of the first five questions is:

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 44

Number of ways in which

3

different numbers in

A . P .

can be selected from

1, 2, 3, \dots \dots . n

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 45

2 m

white identical coins and

2 n

red identical coins are arranged in a straight line with

(m + n)

identical coins on each side of a central mark. The number of ways of arranging the identical coins, so that the arrangements are symmetrical with respect to the central mark.

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 46

The number of ways in which

10

students can be divided into three teams, one containing

4

and others

3

each, is

Let Pn denotes the number of ways of selecting 3 people out of 'n' sitting in a row if no two of them are consecutive and Qn is the corresponding figure when they are in a circle. If Pn-Qn=6, then 'n' is equal to

Important Questions on Permutation and Combination

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Let $P_{n}$ denotes the number of ways of selecting $3$ people out of $' n'$ sitting in a row if no two of them are consecutive and $Q_{n}$ is the corresponding figure when they are in a circle. If $P_{n} - Q_{n} = 6,$ then $' n'$ is equal to