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- Exercise 6.2 (Solutions)
- y ways they be seated at a round table\\ if three particular secretaries want to sit together?\\ [[math-11-nbf:sol:unit06:ex6-2-p11|Solution: Question 18 & 19]] **Question 20.** Find the number of ways that 6 men and 6 women se... alternative seats.\\ [[math-11-nbf:sol:unit06:ex6-2-p12|Solution: Question 20 & 21]] **Question 21.** Make all the permutations of the following word
- Exercise 6.3 (Solutions)
- he following for $n \in \mathbb{N}$.\\ (vi) ${ }^{2 n} \mathrm{C}_{\mathrm{n}}=\frac{2^{n} \cdot[1.3 .5 \ldots(2 n-1)]}{n!}$ (vii) ${ }^{n} C_{p}={ }^{n} C_{q} \Rightarrow p=q$ or $p+q=n$ \\ (viii) ${ }^{n} C_{r}+2{ }^{n} C_{r-1}+{ }^{n} C_{r-2}={ }^{n+2} C_{r}$ (
- Question 8 and 9, Exercise 6.2
- ====== Question 8 and 9, Exercise 6.2 ====== Solutions of Question 8 and 9 of Exercise 6.2 of Unit 06: Permutation and Combination. This is ... an. =====Question 8===== In how many ways can a party of $4$ men and $5$ women be seated at a round ta... ===== How many different signals can be madeWith $2$ blue, $3$ yellow and $4$ green flags using all a
- Question 4, 5 and 6, Review Exercise 6
- x-digit numbers can be formed using the digits $0,2,3,4,5,7$ without repeating? ** Solution. ** Tot... possible permutations of given $6$ digits $$=6!=720$$ Permutations starting with $0$ results into $5... umber,\\ and number of such permutations is $$5!=120$$ Number of $6-$digits numbers formed $$=720-120=600$$ =====Question 5===== The numbers of ways of
- Question 13 and 14, Exercise 6.3
- calculate possible ways if he fails $1$ subject, $2$\\ subject so on upto $6$ subjects.\\ Possible wa... f $6={ }^{6} C_{1}=6$\\ Possible ways of failing $2$ subjects out of $6={ }^{6} C_{2}=15$\\ Possible ways of failing $3$ subjects out of $6={ }^{6} C_{3}=20$\\ Possible ways of failing $4$ subjects outsof
- Review Exercise (Solutions)
- it06:Re-ex6-p1|See MCQs: Question 1]] **Question 2.** How many words can be formed by using $4$ dist... ct alphabets?\\ [[math-11-nbf:sol:unit06:Re-ex6-p2|Solution: Question 2 & 3 ]] **Question 3.** How many $3$-digit numbers are there which has $0$ at unit place?\\ [[math-11-nbf:sol:unit06:Re-ex6-p2|Solution: Question 2 & 3 ]] **Question 4.** How
- Question 5 and 6, Exercise 6.3
- ways can $11$ players be chosen out of $16$ if a particular player is always chosen. ** Solution. ** ... man may be selected ${ }^{5} C_{1}$ ways \\ and $2$ women may be selected in ${ }^{3} C_{2}$ ways.\\ Total possible ways $={ }^{5} C_{1} \times{ }^{3} C_{2}=5 \times 3=15$\\ Case II: If there are $2$ men