Advertisements
Advertisements
प्रश्न
A committee of 5 is to be formed out of 6 gents and 4 ladies. In how many ways this can be done when
- atleast two ladies are included.
- atmost two ladies are included.
उत्तर
(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 |
APPEARS IN
संबंधित प्रश्न
If a polygon has 44 diagonals, find the number of its sides.
How many code symbols can be formed using 5 out of 6 letters A, B, C, D, E, F so that the letters
- cannot be repeated
- can be repeated
- cannot be repeated but must begin with E
- cannot be repeated but end with CAB.
If nPr = 720(nCr), then r is equal to:
There are 10 true or false questions in an examination. Then these questions can be answered in
How many ways can a team of 3 boys,2 girls and 1 transgender be selected from 5 boys, 4 girls and 2 transgenders?
How many different selections of 5 books can be made from 12 different books if, Two particular books are always selected?
There are 5 teachers and 20 students. Out of them a committee of 2 teachers and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees a particular teacher is included?
In an examination a student has to answer 5 questions, out of 9 questions in which 2 are compulsory. In how many ways a student can answer the questions?
A committee of 7 peoples has to be formed from 8 men and 4 women. In how many ways can this be done when the committee consists of at least 3 women?
Find the number of strings of 4 letters that can be formed with the letters of the word EXAMINATION?
