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- Question 18 and 19, Exercise 6.2
- ad, Pakistan. =====Question 18===== Howmany odd numbers less than $10,000$ can be formed using the digits... digits. ** Solution. ** We must make $4$ digit numbers to keep the number less that $10000$\\ and digit ... either $3$ or $5$ to make number odd.\\ Possible numbers starting with $0$ and ending with $3={ }^{3} P=6$\\ Possible numbers starting with $0$ and ending with $5=3 p_{6}=6$\\
- Exercise 6.2 (Solutions)
- ion 3 ]] **Question 4.** How many 3 -digit even numbers can be formed from the digits $1,2,3,4,5,6$, if t... stion 4 & 5 ]] **Question 6.** How many 4 -digit numbers can be formed with the digits $1,2,3,4,5,6$ when ... ution: Question 6 & 7]] **Question 7.** How many numbers can be formed with the digits $1,1,2,2,3,3,4$ so ... Question 14 & 15]] **Question 16.** How many odd numbers can be formed by using the digits $1,2,3,4,5,6$ w
- Question 6 and 7, Exercise 6.2
- kistan. =====Question 6===== How many $4$-digit numbers can be formed with the digits $$1,2,3,4,5,6$ when... times 6=6^4=1296$$ =====Question 7===== How many numbers can be formed with the digits $1,1,2,2,3,3,4$ so ... 7^{\text {th }}$ place.\\ We have to arrange even numbers $2,2,4$ on even places and\\ odd values $1,1,3,3$... !}{2!2!}=\dfrac{24}{4}=6$ $$\text{Total possible numbers }=3 \times 6=18$$ ====Go to ==== <text align="
- Question 16 and 17, Exercise 6.2
- d, Pakistan. =====Question 16===== How many odd numbers can be formed by using the digits $1,2,3,4,5,6$ w... ts of remaining digits.\\ Number of six digit odd numbers $=3 \times{ }^{5} P_{5}=360$ =====Question 17===== How many $4$-digit odd numbers can be formed using the digits $1,2,3,4$ and $5$ ... al, we have $24+24+24=72$ possible $4$ digits odd numbers. ====Go to ==== <text align="left"><btn type
- Question 2 and 3, Review Exercise 6
- 58800$$ =====Question 3===== How many $3$-digit numbers are there which have $0$ at unit place? ** Solution. ** In $3$ digit numbers unit, tens and $100's$ place may be filled in 10 ... digits #0# to $9$.\\ So total possible $3$ digit numbers are $$=10\times 10\times10=1000$$\\ If we fix uni... illed in $10$ ways,\\ so total possible $3-$digit numbers having $0$ at units place are $$=10\times 10=100$
- Question 1, Review Exercise 6
- "a1" collapsed="true">%%(b)%%: $6$</collapse> ii. Numbers of ways of arrangement of the word "GARDEN"\\ ... apse> iii. The product of $r$ consective positive numbers is divisible by \\ * (a) $r!$\\ * (b)$(... " collapsed="true">%%(c)%%: $3$</collapse> x. The numbers of ways in which $r$ latters can be posted in $n$
- Question 4, 5 and 6, Review Exercise 6
- kistan. =====Question 4===== How mant six-digit numbers can be formed using the digits $0,2,3,4,5,7$ with... h permutations is $$5!=120$$ Number of $6-$digits numbers formed $$=720-120=600$$ =====Question 5===== The numbers of ways of arranging $7$ keys in a key chain? **
- Review Exercise (Solutions)
- tion 2 & 3 ]] **Question 3.** How many $3$-digit numbers are there which has $0$ at unit place?\\ [[math-... ion 2 & 3 ]] **Question 4.** How many $6$-digit numbers can be formed using digits $0,2,3,4,5,7$ without ... ution: Question 4, 5 & 6 ]] **Question 5.** The numbers of ways of arranging $7$ keys in a key chain.\\
- Question 4 and 5, Exercise 6.2
- n. =====Question 4===== How many $3$-digit even numbers can be formed from the digits $1,2,3,4,5,6,$ if d... } P_{2}=20$\\ $$\text{Total possible 3-digit even numbers }=20+20+20=60$$ =====Question 5===== How many $7
- Question 12 and 13, Exercise 6.2
- mabad, Pakistan. =====Question 12===== Find the numbers of arrangement of letters of the word VOWEL in wh