Question 1 ( 30 marks) How many different words of five letters can be formed from 7 different consonants and 4 different vowels if no two consonants or vowels can come together and no repetitions are allowed? How many can be formed if each letter could be repeated any number of times? Question 2 ( 30 marks) a) A book club offers a choice of 20 books of which a member chooses six. Find the number of different ways in which a member may make his choice. Given that 12 of the 20 books on offer are novels and that the other 8 are biographies, find the number of different ways in which a member chooses 6 so that i. he/ she has 3 novels and 3 biographies. ii. he/ she has at least 4 biographies b) group of 6 boys and 5 girls are to be photographed together. The girls are to sit on 5 chairs placed in a row and the boys are to stand in a line behind them. Find the number of different possible arrangements. For a second photograph, the boys and girls are to be arranged with 3 boys and 3 girls standing whilst 3 boys and 2 girls are seated on the chairs in front of them, and in each row the boys and girls are to occupy alternate places. Find the number of different possible arrangements.

(Planos) Los ejercicios presentados, a continuación, tienen como objetivo fortalecer nuestro conocimiento en la teoría de planos en el espacio. a) \( \quad \) El punto \( P=(1,2,3) \) pertenece al plano \( a x+b y+\alpha z=15 \), si \( \alpha=1 \) \( \quad \) A=2 \( \mathrm{B}=3 \mathrm{C}=4 \) b) \( \quad \) Dados los siguientes puntos \( A=(a, 2 b,-3 c), B=(5 a, 7 b,-5 c) \) \( C=(-c, 3 a, b) \) Encontrar: L Los ángulos internos del triángulo . ABC

Nedan följer frågor där du ska fylla i saknade siffervärden. Belopp ska anges i tkr. Ett företag startade verksamheten 2021. I början av 2021 köptes inventarier för 600 tkr. Nyttjandeperioden uppskattas till 10 år. I början av 2022 köptes ytterligare inventarier för 200 tkr (även dessa inventarier har en nyttjandeperiod på 10 år). I början av 2023 såldes alla inventarier som anskaffats 2021 för 500 tkr. Ange realisationsresultatet för de sålda inventarierna 2023* 20 tkr Ange beloppet för avskrivningar för 2022** 80 *ange minustecken framför beloppet om det är realisationsförlust **skriv belopp utan minustecken framför

In trabajador gana St, 48,50 diarios y gasta \( 6.5 /, 37,60 \) por dia Si sus ahorros uscienden a Sf. \( 283,40 \). Cuántos dias ha trabajado? \( \begin{array}{lll}36 & \text { B) } 26 & \text { C) } 20\end{array} \)

Refer to functions \( s \) and \( t \). Find the indicated function and write the domain in inte \( s(x)=\frac{x-3}{x^{2}-25} \quad t(x)=\frac{x-5}{3-x} \)

1. Calculate and show your working 1.1 \( 1.2 \frac{3}{3}+\frac{2}{3} \) \( 1.3 \frac{3}{3} \) of 345 \( 1.4350 \div \frac{7}{12} \)