Seven speakers A, B, C, D, E, F, G can deliver speech in,
n = ⁷P₇ = 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1
= 5040 ways.

A = Event that speaker B delivers speech immediately after speaker A.

The favourable outcomes for the event A are obtained as follow:

All 7 speakers can deliver speech in random in the following manners:

• If A comes first, the remaining 6 speakers can deliver their speech in ₆P¹ ways.
• If A comes first and B at second, the remaining 5 speakers can deliver their speech in ₅P¹ ways.
• If C comes after A and B, the remaining 4 speakers can deliver their speech in ₄P¹ ways.
• If D comes after A, B and C, the remaining 3 speakers can deliver their speech in ₃P¹ ways.
• If E comes after A, B, C and D, the remaining 2 speakers can deliver their speech in ₂P¹ ways.
• If F comes after A, B, C, D and E, the speaker G delivers his speech in ₁P¹ ways.

∴ Favourable outcomes for the event A is

m = ₆P¹ × ₅P¹ × ₄P¹ × ₃P¹ × ₂P¹ × ₁P¹

= 6 × 5 × 4 × 3 × 2 × 1 = 720

Hence. P(A) = \(\frac{m}{n} = \frac{720}{5040} = \frac{1}{7}\)

Alternative Method:
Seven speakers A, B, C, D, E, F, G can deliver speech in n = ₇P⁷ = 7! = 5040 ways.

A = Event that speaker B delivers speech immediately after speaker A.

The favourable outcomes for A are obtained as follows:
Considering speakers A and B as one unit, total 6 speakers can deliver speech in ₆P⁶ ways and B can deliver speech immediately after speaker A in ₁P¹ way.

∴ Favourable outcomes for A

m = ₆P⁶ × ₁P¹

= 6! × 1 = 720

∴ P(A) = \(\frac{m}{n} = \frac{720}{5040} = \frac{1}{7}\)