including jose, there are eight people in his family. if order matters, how many ways can he arrange his…

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?\n35\n840\n1,680\n2,620

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?\n35\n840\n1,680\n2,620

Answer

Explanation:

Step1: Fix Jose's position

Since Jose must sit in the first - seat, there is 1 way to place him.

Step2: Calculate remaining arrangements

We need to arrange 4 seats out of the remaining 7 family members. The number of permutations of (n) objects taken (r) at a time is given by the formula (P(n,r)=\frac{n!}{(n - r)!}). Here, (n = 7) and (r=4). [P(7,4)=\frac{7!}{(7 - 4)!}=\frac{7!}{3!}=\frac{7\times6\times5\times4\times3!}{3!}=7\times6\times5\times4 = 840]

Answer:

840