Answer:
(c) 0.325
Step-by-step explanation:
Given,
The number of bolts = 12,
Numbers of nuts = 10,
Total items = 12 + 10 = 22
Thus, the number of ways of choosing 8 items out of 22 items = C(22,8)
Now, the number of ways of choosing 4 bolts and 4 nuts = C(12, 4) × C(10, 4)
Hence, the probability of getting four bolts and four nuts
[tex]=\frac{\text{ways of choosing 4 nuts and 4 bolts}}{\text{Total ways of choosing 8 items}}[/tex]
[tex]=\frac{C(12,4)\times C(10,4)}{C(22, 8)}[/tex]
[tex]=\frac{\frac{12!}{4!8!}\times \frac{10!}{4!6!}}{\frac{22!}{8!14!}}[/tex]
[tex]=\frac{495\times 210}{319770}[/tex]
[tex]=0.325077399381[/tex]
[tex]\approx 0.325[/tex]
Therefore, option (c) is correct.
