Shamoon preguntado en Science & MathematicsMathematics · hace 3 meses

# How many different linear arrangements are there of the digits 1, 2, 3, 4, 5, 6 for which:  (a) 5 and 6 are next to each other ?

### 3 respuestas

Relevancia
• hace 3 meses

5P5 * 2 =

5!/(5 - 5)! * 2 =

5! * 2 =

240

• Pope
Lv 7
hace 3 meses

There are six elements in the set. The 5 and 6 must be adjacent, so they are taken as an inseparable pair, a single element. There are now five elements, which can be arranged in 5! distinct orders. The pair (5,6) can be arranged in 2! orders.

(5!)(2!) = 240

• hace 3 meses

Each of the following scenarios show 5 and 6, as well as 6 and 5, next to each other.  That will give 2 possibilities permuted with the remaining 4 digits.

Positions 1 and 2 give: 2x4x3x2x1 = 48

Positions 2 and 3 give: 2x4x3x2x1 = 48

Positions 3 and 4 give: 2x4x3x2x1 = 48

Positions 4 and 5 give: 2x4x3x2x1 = 48

Positions 5 and 6 give: 2x4x3x2x1 = 48

5x48 = 240

¿Aún tienes preguntas? Pregunta ahora para obtener respuestas.