A) 123 | B) 113 |

C) 246 | D) 945 |

Explanation:

A Committee of 5 persons is to be formed from 6 gentlemen and 4 ladies by taking.

(i) 1 lady out of 4 and 4 gentlemen out of 6

(ii) 2 ladies out of 4 and 3 gentlemen out of 6

(iii) 3 ladies out of 4 and 2 gentlemen out of 6

(iv) 4 ladies out of 4 and 1 gentlemen out of 6

In case I the number of ways = = 4 x 15 = 60

In case II the number of ways = = 6 x 20 = 120

In case III the number of ways = = 4 x 15 = 60

In case IV the number of ways = = 1 x 6 = 6

Hence, the required number of ways = 60 + 120 + 60 + 6 = 246

A) F is third to the left of B | B) F is second to the right of B |

C) B is an immediate neighbour of D | D) All of the above |

Explanation:

From the given information, the circular arrangement is

Here F is second to the right of B and the remaning all are wrong.

A) 43929 | B) 59049 |

C) 15120 | D) 0 |

Explanation:

Number of words with 5 letters from given 9 alphabets formed =

Number of words with 5 letters from given 9 alphabets formed such that no letter is repeated is =

Number of words can be formed which have at least one letter repeated = -

= 59049 - 15120

= 43929

A) 5040 | B) 3650 |

C) 4150 | D) 2520 |

Explanation:

Total number of letters in the word ABYSMAL are 7

Number of ways these 7 letters can be arranged are 7! ways

But the letter is repeated and this can be arranged in 2! ways

=> Total number of ways arranging ABYSMAL = 7!/2! = 5040/2 = 2520 ways.

A) 186 | B) 144 |

C) 136 | D) 120 |

Explanation:

In given word OLIVER there are 3 vowels E, I & O. These can be arranged in only one way as dictionary order E, I & O.

There are 6 letters in thegiven word.

First arrange 3 vowels.

This can be done in 6C3 ways and that too in only one way.(dictionary order E, I & O)

Remaining 3 letters can be placed in 3 places = 3! ways

Total number of possible ways of arranging letters of OLIVER = 3! x 6C3 ways

= 6x5x4 = 120 ways.

A) 120 | B) 256 |

C) 192 | D) 244 |

Explanation:

We are having with digits 2, 3, 4, 5 & 6 and numbers greater than 4000 are to be formed, no digit is repeated.

The number can be 4 digited but greater than 4000 or 5 digited.

Number of 4 digited numbers greater than 4000 are

4 or 5 or 6 can occupy thousand place => 3 x 4P3 = 3 x 24 = 72.

5 digited numbers = 5P5 = 5! = 120

So the total numbers greater than 4000 = 72 + 120 = 192