From a group of 6 boys and 4 girls, four children are to be selected. In how many ways can the selection be made such that at least one boy is included?

Problem restatement
Select 4 children from 6 boys and 4 girls with the restriction that the selection contains at least one boy.

Given data

• Boys = 6
• Girls = 4
• Total to choose = 4

Concept/Approach
Count total 4-child selections and subtract the disallowed case (all girls). Use combinations nCk.

Step-by-Step calculation
Total selections = ⁡10C4 = 210Disallowed (0 boy) = ⁡4C4 = 1Valid selections = 210 − 1 = 209

Verification/Alternative
Casewise sum: (1B,3G) + (2B,2G) + (3B,1G) + (4B,0G) = ⁡6C1⁡4C3 + ⁡6C2⁡4C2 + ⁡6C3⁡4C1 + ⁡6C4⁡4C0 = 24 + 90 + 80 + 15 = 209.

Common pitfalls
Forgetting to subtract the all-girls selection, or miscounting with permutations instead of combinations.

Final Answer
209