A) 2 x (17!) | B) 2 x (18!) |

C) (3!) x (18!) | D) (17!) |

Explanation:

A person can be choosen out of 18 people in 18 ways to be seated between Musharraf and Manmohan. Now consider Musharraf , Manmohan and the third person, sitting between them, as a single personality, we can arrange them in 17! ways but Musharraf and Manmohan can also be arranged in 2 ways.

Required number of permutations = 18 x (17!) x 2 = 2 x 18!

A) 600 | B) 610 |

C) 609 | D) 599 |

Explanation:

Two men, three women and one child can be selected in ⁴C₂ x ⁶C₃ x ⁵C₁ ways

=

= 600 ways.

A) 2580 | B) 3687 |

C) 4320 | D) 5460 |

Explanation:

Let 'Y' be the youngest player.

The last song can be sung by any of the remaining 3 players. The first 3 players can sing the song in (3!) ways.

The required number of ways = 3(3!) = 4320.

A) 215 | B) 268 |

C) 254 | D) 216 |

Explanation:

Since each ring consists of six different letters, the total number of attempts possible with the three rings is = 6 x 6 x 6 = 216. Of these attempts, one of them is a successful attempt.

Maximum number of unsuccessful attempts = 216 - 1 = 215.

A) 2(6!) | B) 6! x 7 |

C) 6! x ⁷P₆ | D) None |

Explanation:

We can initially arrange the six boys in 6! ways.

Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.

Hence required number of ways = 6! x ⁷P₆

A) 9!/(2!)^{2}x3! | B) 9! x 2! x 3! |

C) 0 | D) None |

Explanation:

n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.

The letter pattern 'MESMERISE' consists of 10 letters of which there are 2M's, 3E's, 2S's and 1I and 1R.

Number of arrangements =