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Question 7 and 8, Exercise 6.3 @math-11-nbf:sol:unit06
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has exactly $2$ women. ** Solution. ** (i) If there are exactly $2$ women then there will be $3$ man in committee. Total possible ways $={ }^{4} C_{2} \tim... women. ** Solution. ** At least $2$ women means there could be more than $2$ women as well.\\ So we wil... having $2,3$ and four women in committee.\\ So if there are $2$ women we already had calculated $120$ pos
Question 23 and 24, Exercise 4.3 @math-11-nbf:sol:unit04
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rchers are in the last row? How many marchers are there altogether? ** Solution. ** From the statement,... $62$ marchers in last row and $950$ marchers are there altogether. GOOD m( =====Question 24===== How m... any poles will be in a pile of telephone poles if there are 50 in the first layer, 49 in the second and so on, until there are 6 in the last layer? ** Solution. ** From t
Question 5 and 6, Exercise 6.3 @math-11-nbf:sol:unit06
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ny ways can $11$ players be chosen out of $16$ if there is no restriction. ** Solution. ** $11$ players... in ${ }^{16} C_{11}$ ways.\\ i.e. $4368$ ways are there to choose $11$ players.\\ =====Question 5(ii)===... ? ** Solution. ** Case I: If one man is chosen there will be two women in committee.\\ $1$ man may be ... \times{ }^{3} C_{2}=5 \times 3=15$\\ Case II: If there are $2$ men and one woman in committee. Total po
Question 2, Exercise 2.5 @math-11-nbf:sol:unit02
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} \\ 0 & 0 & 1 \end{array} \right] \end{align*} There are $3$ non-zero rows.\\ The rank of the matrix i... nd{array} \right] \quad R3 - 12R2 \\ \end{align*} There are $2$ non-zero rows.\\ The rank of the matrix i... rray} \right] \quad \frac{3}{124}R3 \end{align*} There are $3$ non-zero rows.\\ The rank of the matrix i... \right] \quad R1 - 3R2, \, R3 - 3R2 \end{align*} There are $2$ non-zero rows.\\ The rank of the matrix i
Exercise 6.3 (Solutions) @math-11-nbf:sol:unit06
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ways can 11 players be chosen out of 16 if\\ (i) there is no restriction. (ii) a particular player is al... -3-p7|Solution: Question 7 & 8]] **Question 8.** There are 10 points on a circle. Find the number of $(\... 2]] **Question 12.** For the post of 6 officers, there are 100 applicants, 2 posts are reserved for serv
Question 11 and 12, Exercise 4.2 @math-11-nbf:sol:unit04
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f the pattern is consistent, how many plants will there be in the eighth row? ** Solution. ** Given seq... lign*} Hence $a_8=7$, that is, $7$ plants will be there in the 8th row. GOOD ====Go to ==== <text align
Question 11 and 12, Exercise 6.3 @math-11-nbf:sol:unit06
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===Question 12===== For the post of $6$ officers, there are $100$ appliciants,\\ $2$ posts are reserved f... serving candidiates and remaining for others. \\ There are $20$ serving candidates among the appliciants
Unit 06: Permutation and Combination @math-11-nbf:sol
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on of $n$ different objects taken $r$ at a time. There are four exercises in this chapter. * **[[math
Question 1, Exercise 2.6 @math-11-nbf:sol:unit02
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\end{align*} With the different values of $x_3$, there are infinite solutions. Hence solution is; \beg
Question 4, Exercise 2.6 @math-11-nbf:sol:unit02
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} R_2 \text{ by 11 and } R_3 - R_2). \end{align*} There is no value of $x$. Then $x_3 = 0$. From the s
Question 12 and 13, Exercise 6.2 @math-11-nbf:sol:unit06
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Possible arrangements of $7$ letters $=71=5040$\\ There are $3$ vowels $A, I$ and $E$ in word.\\ To find
Question 16 and 17, Exercise 6.2 @math-11-nbf:sol:unit06
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rangements and\\ similarly for $5$ at units place there are $24$ arrangements.\\ Hence in total, we have
Question 2 and 3, Review Exercise 6 @math-11-nbf:sol:unit06
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===Question 3===== How many $3$-digit numbers are there which have $0$ at unit place? ** Solution. **
Review Exercise (Solutions) @math-11-nbf:sol:unit06
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] **Question 3.** How many $3$-digit numbers are there which has $0$ at unit place?\\ [[math-11-nbf:sol