To solve the problem, we use the principle of inclusion-exclusion for three sets.

Step 1: Recall the inclusion-exclusion formula

For three sets (A, B, C):
[|A \cup B \cup C| = |A| + |B| + |C| - |A∩B| - |A∩C| - |B∩C| + |A∩B∩C|]

Given:

• (|A \cup B \cup C| = 100) (everyone has at least one skill),
• (|A|=60, |B|=60, |C|=70),
• (|A∩B|=|A∩C|=|B∩C|=40),
• Let (x = |A∩B∩C|) (the number of people with all three skills).

Step 2: Substitute values into the formula

[100 = 60 + 60 + 70 - 40 - 40 - 40 + x]

Step 3: Simplify and solve for (x)

[100 = (60+60+70) - (40×3) + x]
[100 = 190 - 120 + x]
[100 = 70 + x]
[x = 30]

Answer: (\boxed{30})

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