Question 22 and 23, Exercise 6.2

Solutions of Question 22 and 23 of Exercise 6.2 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.

Encrypt the word LAHORE by using the permutation: $(3\quad 4\quad 6\quad 1\quad 5\quad2)$ by labelling L as $1$ and A as $2$ and so on.

Solution.

$L=1, A=2, H=3, O=4, R=5, E=6$
Now $(3,4,6,1,5,2)=$ HOELRA

Decrypt the word “TNLUMA” by using the permutation: $(4\quad 6\quad 3\quad 2\quad 1\quad5)$.

Solution.

$(4,6,3,2,1,5)$ mean place first letter of given word at $4^{\text {th }}$ position,
place $2^{\text {nd }}$ letter at $6^{\text {th }}$ position,
$3^{\text {rd }}$ letter at $3^{\text {rd }}$ position,
$4^{\text {th }}$ letter at $2^{\text {nd }}$ position,
$5^{\text {th }}$ letter at $1^{\text {st }}$. position,
$6^{\text {th }}$ letter at $5^{\text {th }}$ position. i.e., $$(4,6,3,2,1,5)=\text { MULTAN }$$

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