A) 100 | B) 200 |

C) 300 | D) 400 |

Explanation:

Since 8 does not occur in 1000, we have to count the number of times 8 occurs when we list the integers from 1 to 999. Any number between 1 and 999 is of the form xyz, where $0\le x,y,z\le 9.$

Let us first count the numbers in which 8 occurs exactly once.

Since 8 can occur atone place in $3{C}_{1}$ways. There are $3x9x9$ such numbers.

Next, 8 can occur in exactly two places in $3{C}_{2}\times 9$ such numbers. Lastly, 8 can occur in all three digits in one number only.

Hence, the number of times 8 occur is

$1\times \left(3\times {9}^{2}\right)+2\times \left(3\times 9\right)+3\times 1=300$

A) 1,51,200 ways. | B) 5,04,020 ways |

C) 72,000 ways | D) None of the above |

Explanation:

In circumcstances word there are 3C's, 2S's, I, U,R, T, A, N, E

Total = 13 letters

But last letter must be N

Hence, available places = 12

In that odd places = 1, 3, 5, 7, 9, 11

Owvels = 4

This can be done in **6P4 ways **

Remaining 7 letters can be arranged in** 7!/3! x 2! ways**

Hence, total number of ways = **6P4 x 7!/3! x 2! = 360 x 5040/12 = 1,51,200 ways.**

A) 720 | B) 5040 |

C) 360 | D) 180 |

Explanation:

The number of letters in the given word RITUAL = 6

Then,

Required number of different ways can the letters of the word 'RITUAL' be arranged = 6!

**=> 6 x 5 x 4 x 3 x 2 x 1 = 720**

A) 64 | B) 63 |

C) 62 | D) 60 |

Explanation:

Given digits are 0, 4, 2, 6

Required 4 digit number should be greater than 6000.

So, first digit must be 6 only and the remaining three places can be filled by one of all the four digits.

This can be done by

1x4x4x4 = 64

Greater than 6000 means 6000 should not be there.

Hence, 64 - 1 = 63.

A) 15/52 | B) 17/26 |

C) 13/17 | D) 15/26 |

Explanation:

Number of cards in a pack of cards = 52

Number of black cards = 26

Number of king cards = 4 (2 Red, 2 Black)

Required, the probability that if a card is drawn either card is black or a king =

$\frac{26}{52}+\frac{4}{52}=\frac{30}{52}=\frac{15}{26}$

A) 48 | B) 24 |

C) 64 | D) 32 |

Explanation:

Total number of balls = 2 + 3 + 4 = 9

Total number of ways 3 balls can be drawn from 9 = 9C3

No green ball is drawn = 9 - 3 = 6 = 6C3

Required number of ways if atleast one green ball is to be included = Total number of ways - No green ball is drawn

= 9C3 - 6C3

= 9x8x7/3x2 - 6x5x4/3x2

= 84 - 20

**= 64 ways.**

A) 60 | B) 48 |

C) 36 | D) 20 |

Explanation:

Here given the required digit number is 4 digit.

It must be divisible by 5. Hence, the unit's digit in the required 4 digit number must be 0 or 5. But here only 5 is available.

**x x x 5**

The remaining places can be filled by remaining digits as 5 x 4 x 3 ways.

Hence, number 4-digit numbers can be formed are **5 x 4 x 3 = 20 x 3 = 60.**

A) 720 | B) 360 |

C) 120 | D) 24 |

Explanation:

Given word is SCOOTY

ATQ,

Except S & Y number of letters are 4(C 2O's T)

Hence, required number of arrangements** = 4!/2! x 2! = 4! **

**= 4 x 3 x 2 **

**= 24 ways.**

A) 3360 | B) 5040 |

C) 720 | D) 1080 |

Explanation:

Given word is GLACIOUS has 8 letters.

=> **C** is fixed in one of the 8 places

Then, the remaining 7 letters can be arranged in **7! ways = 5040.**