A group has 8 men and 7 women. In how many ways can a committee of 5 people be formed if the number of women is at least 3?
A
785
B
988
C
1281
D
1125
উত্তরের বিবরণ
Question: A group has 8 men and 7 women. In how many ways can a committee of 5 people be formed if the number of women is at least 3?
Solution:
Given that,
Total committee size = 5
And for women ≥ 3, possible distributions:
Three ways to formed the committee
1. 3 women + 2 men
2. 4 women + 1 man
3. 5 women + 0 men
Now, 1st case- 3 women + 2 men
Choose 3 women from 7, (7C3) = 35
Choose 2 men from 8, (8C2) = 28
∴ Total ways = 35 × 28 = 980
2nd case- 4 women + 1 man
Choose 4 women from 7, (7C4) = 35
Choose 1 man from 8, (8C1) = 8
∴ Total ways = 35 × 8 = 280
And 3rd case-5 women + 0 men
Choose 5 women from 7, (7C5) = 21
No men to choose
∴ Total ways = 21
∴ Total ways = 980 + 280 + 21= 1281
0
Updated: 18 hours ago
Three unbiased coins are tossed. What is the probability of getting at least 2 heads?
Created: 18 hours ago
A
1/4
B
2/3
C
1/2
D
1/3
Question: Three unbiased coins are tossed. What is the probability of getting at least 2 heads?
Solution:
Total outcomes = {TTT, TTH,THT, HTT, THH, HTH, HHT, HHH} = 8
Favorable outcomes = {HHT, HTH, THH, HHH} = 4
So, the probability of getting at least 2 heads = Favorable outcomes/Total outcomes
= 4/8 = 1/2
0
Updated: 18 hours ago
Two cards are drawn at random and without replacement from a standard deck of 52 cards. What is the probability that both cards are face cards?
Created: 18 hours ago
A
1/26
B
1/13
C
5/52
D
11/221
Question: Two cards are drawn at random and without replacement from a standard deck of 52 cards. What is the probability that both cards are face cards?
Solution:
Total card = 52
Total face card = 3 × 4 = 12
Total ways to choose 2 cards from 52 = 52C2 = (52 × 51)/2 = 1326
Total ways to choose 2 face cards from 12 = 12C2 = (12 × 11)/2 = 66
∴ So, the probability that both cards are face cards = 66/1326
= (2 × 3 × 11)/(2 × 3 × 221)
= 11/221
0
Updated: 18 hours ago
m বাস্তব সংখ্যা এবং 5m - 2 > - 12 হলে নিচের কোনটি সঠিক?
Created: 12 hours ago
A
m ∈ (2, ∞)
B
m ∈ (2, - 2)
C
m ∈ (- 2, ∞)
D
m ∈ (- 3, ∞)
সমাধান:
5m - 2 > - 12
⇒ 5m > - 12 + 2
⇒ 5m > - 10
⇒ m > - (10/5)
∴ m > - 2
∴ সঠিক উত্তর: m ∈ (- 2, ∞)
0
Updated: 12 hours ago
