Explanation:

- Initially, we have a group of students with an average height of 156 cm.

- Five more students with an average height of 160 cm join the group.

- After their addition, the group’s average height increases by 0.8 cm.

- Let the initial number of students be denoted by \( n \).

- The total height of the initial group is \( 156n \).

- The total height of the new students is \( 5 \times 160 = 800 \).

- The total number of students now is \( n + 5 \).

- The new average height of the group is \( 156 + 0.8 = 156.8 \).

Set up the equation:

$$ \frac{156n + 800}{n + 5} = 156.8 $$

Solve for \( n \):

$$ 156n + 800 = 156.8(n + 5) $$

$$ 156n + 800 = 156.8n + 784 $$

$$ 800 - 784 = 156.8n - 156n $$

$$ 16 = 0.8n $$

$$ n = \frac{16}{0.8} $$

$$ n = 20 $$

- Option 3: 20 is correct.

.