Tamil Nadu Board of Secondary EducationHSC Commerce Class 11

# A committee of 5 is to be formed out of 6 gents and 4 ladies. In how many ways this can be done when (i) atleast two ladies are included. (ii) atmost two ladies are included. - Business Mathematics and Statistics

Sum

A committee of 5 is to be formed out of 6 gents and 4 ladies. In how many ways this can be done when

1. atleast two ladies are included.
2. atmost two ladies are included.

#### Solution

(i) A committee of 5 is to be formed.

 Possibilities Ladies (4) Gents (6) Combinations 1 2 3 4"C"_2 xx 6"C"_3 = (4xx3)/(2xx1) xx (6xx5xx4)/(3xx2xx1) = 120 1 4 4"C"_1 xx 6"C"_4 = 4 xx 6"C"_2 = 4 xx (6xx5)/(2xx1) = 60 0 5 4C0 × 6C5 = 1 × 6C1 = 1 × 6 = 6 Total number of ways = 186

(ii) Almost two ladies are included means maximum of two ladies are included.

 Possibilities Ladies (4) Gents (6) Combinations 1 2 3 4"C"_2 xx 6"C"_3 = (4xx3)/(2xx1) xx (6xx5xx4)/(3xx2xx1) = 120 2 3 2 4"C"_3 xx 6"C"_2 = (4xx3xx2)/(3xx2xx1) xx (6xx5)/(2xx1) = 60 3 4 1 4C4 × 6C1 = 1 × 6 = 6 Total number of ways = 186
Concept: Combinations
Is there an error in this question or solution?
Chapter 2: Algebra - Exercise 2.4 [Page 38]

Share