Question

The number of ways in which 5 days can be chosen in each of the 12 months of a non-leap year, is:
1. (³⁰C₅)⁴ × (³¹C₅)⁷ × (²⁸C₅)
2. (30C5)6 × (28C3. (30C5)7 × (31C4. (30C5)5 × (31C<span style="position: rel

Answer 1

Correct Answer - Option 1 : (³⁰C₅)⁴ × (³¹C₅)⁷ × (²⁸C₅)

Concept:

• There are 29 days in the month of February in a leap year and 28 days in a non-leap year. Other months have either 30 or 31 days.

• The number of ways in which r distinct objects can be selected from a group of n distinct objects, is:

  ⁿC_r = \(\rm \frac {n!}{r!(n-r)!}\).

  n! = 1 × 2 × 3 × ... × n.

  0! = 1.

 

Calculation:

The months and their number of days, in a non-leap year, are listed in the following table:

Month	Number of days
January	31
February	28
March	31
April	30
May	31
June	30
July	31
August	31
September	30
October	31
November	30
December	31

 

There are 1 month with 28 days, 4 months with 30 days and 7 months with 31 days.

The required number of selecting 5 days from each of them would be:

(30C5)4 × (31C5)7 × (28C5)