====== Question 14 and 15 Exercise 6.2 ====== Solutions of Question 14 and 15 of Exercise 6.2 of Unit 06: Permutation, Combination and Probablity. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 14===== If five distinct keys are placed on a key ring, how many different orders are possible? ====Solution==== The total different possible orders are: $$\dfrac{(n-1) !}{2}=\dfrac{(5-1) !}{2}=\dfrac{24}{2}=12 $$ =====Question 15===== In how many ways can $7$ people be arranged at a round table so that 2 particular persons always sit together? ====Solution==== Nurnber of ways in which $7$ people can be seated around a round table without any condition is $6 !$ Now, let us assume these two particular people ALWAYS sit together and let us consider them as one unit. Number of ways in which $6$ people can be arranged around a round table is $5!$ And the two particular people can be arranged between them selves in $2 !=2$ ways. Hence, number of ways in which $7$ people can sit around a round table where the two people must not sit together is: $$2 \times 5 !=240$$ ====Go To==== [[math-11-kpk:sol:unit06:ex6-2-p9 |< Question 13 ]]