A) 109 | B) 190 |

C) 901 | D) 910 |

Explanation:

Number of positive integral solutions =

=

= 190

A) 59 | B) 60 |

C) 61 | D) 64 |

Explanation:

The given digits are 1, 2, 3, 5, 7, 9

A) 3/17 | B) 4/21 |

C) 2/21 | D) 5/17 |

Explanation:

Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.

Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 x 2)/(15 x 14) = 1/35

Probability that both are yellow = ²C₂/¹⁵C₂ = (2 x 1)/(15 x 14) = 1/105

Probability that one blue and other is yellow = (³C₁ x ²C₁)/¹⁵C₂ = (2 x 3 x 2)/(15 x 14) = 2/35

Required probability = 1/35 + 1/105 + 2/35

= 3/35 + 1/105 = 1/35(3 + 1/3)

= 10/(3 x 35) = 2/21

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.