Question

question 2 (1 point) how many ways can 6 friends stand together in a line if tigger and roo must stand together?

Explanation:

Step1: Treat Tigger and Roo as a single unit

Since Tigger and Roo must stand together, we consider them as one combined entity. So now we have to arrange 5 units (the Tigger - Roo unit and the other 4 friends) in a line. The number of ways to arrange \( n \) distinct units in a line is \( n! \). Here \( n = 5 \), so the number of arrangements of these 5 units is \( 5! \).

Step2: Arrange Tigger and Roo within their unit

Within the Tigger - Roo unit, Tigger and Roo can be arranged in \( 2! \) ways (either Tigger first then Roo or Roo first then Tigger).

Step3: Calculate the total number of arrangements

By the multiplication principle, the total number of ways to arrange the 6 friends with Tigger and Roo together is the product of the number of ways to arrange the 5 units and the number of ways to arrange Tigger and Roo within their unit. So we calculate \( 5! \times 2! \).
We know that \( n! = n\times(n - 1)\times\cdots\times1 \), so \( 5! = 5\times4\times3\times2\times1=120 \) and \( 2! = 2\times1 = 2 \). Then \( 5! \times 2! = 120\times2=240 \).

Answer:

240