Question

including jose, there are eight people in his family. if order matters, how many ways can he arrange his family members into a row of five seats if jose must sit in the first seat? 35 840 1,680 2,620

Explanation:

Step1: Fix Jose in first seat

Total remaining people: $8-1=7$

Step2: Fill 4 remaining seats

We use permutations: $P(7,4) = 7 \times 6 \times 5 \times 4$

Step3: Calculate the product

$7 \times 6 = 42$; $42 \times 5 = 210$; $210 \times 4 = 840$

Answer:

840