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In how many ways can a selection of 6 out of 4teachers and 8 students be done so as toinclude atleast two teachers?
- a)220
- b)672
- c)896
- d)968
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
In how many ways can a selection of 6 out of 4teachers and 8 students ...
Given: 4 teachers and 8 students, 6 people to be selected with at least 2 teachers.
To find: Number of ways to select 6 people with at least 2 teachers.
Solution:
We can use the principle of inclusion-exclusion to solve this problem.
Total number of ways to select 6 people from 12 = 12C6 = 924
Number of ways to select 6 people with no teachers = 8C6 = 28
Number of ways to select 6 people with only 1 teacher = (4C1 * 8C5) = 672
Using inclusion-exclusion principle, the number of ways to select 6 people with at least 2 teachers is:
= Total number of ways to select 6 people - Number of ways to select 6 people with no teachers - Number of ways to select 6 people with only 1 teacher
= 924 - 28 - 672
= 224
Therefore, the correct option is (b) 672.
To find: Number of ways to select 6 people with at least 2 teachers.
Solution:
We can use the principle of inclusion-exclusion to solve this problem.
Total number of ways to select 6 people from 12 = 12C6 = 924
Number of ways to select 6 people with no teachers = 8C6 = 28
Number of ways to select 6 people with only 1 teacher = (4C1 * 8C5) = 672
Using inclusion-exclusion principle, the number of ways to select 6 people with at least 2 teachers is:
= Total number of ways to select 6 people - Number of ways to select 6 people with no teachers - Number of ways to select 6 people with only 1 teacher
= 924 - 28 - 672
= 224
Therefore, the correct option is (b) 672.
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Community Answer
In how many ways can a selection of 6 out of 4teachers and 8 students ...
Number of ways to select 6 out of 4 teachers and 8 students such there are atleast 2 teachers
4C2 × 8C4 + 4C3 × 8C3 + 4C4 × 8C2
= 420 + 224 + 28
= 672
4C2 × 8C4 + 4C3 × 8C3 + 4C4 × 8C2
= 420 + 224 + 28
= 672
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In how many ways can a selection of 6 out of 4teachers and 8 students be done so as toinclude atleast two teachers?a)220b)672c)896d)968Correct answer is option 'B'. Can you explain this answer?
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