Question

7 speakers A, B, C, D, E, F and G are Invited to deliver a speech in a program. Speakers have to deliver speech one after the other. In how many ways, speeches of 7 speakers can be arranged If the speaker B has to deliver his speech Immediately after the speaker A?

Answer 1

7 speakers A, B. C. D, E, F. G have to deliver speech one after the other. If the speaker A delivers lits speech first. the remaining 6 speakers can be arranged for their speech in ⁶P₁ ways.

If B delivers his speech after the speaker A. the remaIning 5 speakers can be arranged for their speech In ⁵P₁ ways.

If C delivers his speech after the speakers A and B, the remaining 4 speakers can be arranged for their speech in ⁴P₁ ways.

If D delivers his speech after the speakers A, B and C, the remaIning 3 speakers can be arranged for their speech in ³P₁ ways.

If E delivers his speech after the speakers A, B, C and D, the remalng 2 speakers can be arranged for their speech in ²P₁ ways.

Not, at the last the speaker F can deliver his speech after the speakers A, B, C, D and E, have delivered their speech in ¹P₁ ways.

∴ Total permutations

= ⁶P₁ × ⁵P₁ × ⁴P₁ × ³P₁ × ²P₁ × ¹P₁

= 6 × 5 × 4 × 3 × 2 × 1

= 720