# Permutations and Combinations Questions

A) 376 | B) 375 |

C) 500 | D) 673 |

Explanation:

The smallest number in the series is 1000, a 4-digit number.

The largest number in the series is 4000, the only 4-digit number to start with 4.

The left most digit (thousands place) of each of the 4 digit numbers other than 4000 can take one of the 3 values 1 or 2 or 3.

The next 3 digits (hundreds, tens and units place) can take any of the 5 values 0 or 1 or 2 or 3 or 4.

Hence, there are 3 x 5 x 5 x 5 or 375 numbers from 1000 to 3999.

Including 4000, there will be 376 such numbers.

A) 25200 | B) 52000 |

C) 120 | D) 24400 |

Explanation:

Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)

=

= 210.

Number of groups, each having 3 consonants and 2 vowels = 210.

Each group contains 5 letters.

Number of ways of arranging 5 letters among themselves

= 5!

= 120

Required number of ways = (210 x 120) = 25200.

A) 196 | B) 186 |

C) 190 | D) 200 |

Explanation:

When at least 2 women are included.

The committee may consist of 3 women, 2 men : It can be done in ways

or, 4 women, 1 man : It can be done in ways

or, 2 women, 3 men : It can be done in ways.

Total number of ways of forming the committees

=

= 6 x 20 + 4 x 15 + 1x 6

= 120 + 60 + 6 =186

A) 4050 | B) 3600 |

C) 1200 | D) 5040 |

Explanation:

'LOGARITHMS' contains 10 different letters.

Required number of words = Number of arrangements of 10 letters, taking 4 at a time.

=

= 5040.

A) 601 | B) 600 |

C) 603 | D) 602 |

Explanation:

If the word started with the letter A then the remaining 5 positions can be filled in 5! Ways.

If it started with c then the remaining 5 positions can be filled in 5! Ways.Similarly if it started with H,I,N the remaining 5 positions can be filled in 5! Ways.

If it started with S then the remaining position can be filled with A,C,H,I,N in alphabetical order as on dictionary.

The required word SACHIN can be obtained after the 5X5!=600 Ways i.e. SACHIN is the 601th letter.