Answer : This is a case of combination: Here, n=25 r=4 ⇒ nCr= 25C4 ⇒25C4=12650 possible ways. Ans: In 12650 ways, from a class of 25 students, 4 can be chosen for a competition. ...
Answer : Number of points=21 ⇒n=21 A chord connects circle at two points. ⇒r=2 ⇒Number of chords from 21 points= nCr ⇒ nCr= 21C2 ⇒21C2=210 chords. Ans: 210 chords can be drawn through 21 points on a...
Answer : With 12 people , we need to choose a subset of two different people where order does not matter. Also, we need to choose all such subsets because each person is shaking hands with everyone...
Answer : Condition: Each student has an equal chance of getting selected. Imagine selecting the teammates one at a time. There are 15 ways of selecting the first teammate, 14 ways of selecting the...
Answer : Given: n+1Cr+1 : nCr = 11 : 6 and nCr : n–1Cr–1 = 6 : 3 To Find : n & r We use this property in this question: ⇒6(n+1)=11(r+1) ⇒6n+6=11r+11 ⇒6n-11r=5 …(1) nCr : n–1Cr–1 = 6 : 3 ⇒...
Answer : Given, nCr–1 = 36, nCr = 84 and nCr+1 = 126 To find:r=? ⇒2(n-r)=3(r+1) ⇒2n-5r=3….(2) From equations 1 & 2 we get n=9 & r=3 Ans: r = 3
Answer : Given: nPr = 840 and nCr = 35 To find: r=? We know that: ⇒ nPr= nCr×r! ⇒840=35×r! ⇒r!=4! ⇒r=4 Ans: r = 4
Answer : Given: 15Cr : 15Cr–1 = 11 : 5 To find: r=? 15Cr : 15Cr–1 = 11 : 5 ⇒5×(16-r)=11r ⇒80-5r=11r ⇒16r=80 ⇒r=5 Ans: r = 5
Answer : Given: 2nC3: nC3 = 12 : 1 To find: n=? 2nC3: nC3 = 12 : 1 ⇒2n-1=3(n-2) ⇒2n-1=3n-6 ⇒n=6-1=5 Ans: n = 5
Answer : Given: nCr–1 = nC3r To find: r=? We know that: nCr = nCn-r ⇒ nCr–1 = nCn-(r-1) ⇒ nCr–1 = nCn-r+1 ⇒ nCn-r+1= nC3r ⇒n-r+1=3r ⇒4r=n+1
Answer : Given: 20Cr = 20Cr+6 To find: r=? We know that: nCr = nCn-r ⇒ 20Cr+6= 20C20-(r+6) ⇒ 20Cr+6= 20C20-r-6=20C14-r ⇒ 20C14-r= 20Cr ⇒14-r=r ⇒2r=14 Ans:r=7 (ii) Given: 18Cr = 18Cr+2 To find: rC5=?...
Answer : Given: nC7 = nC5 To find : n=? We know that: nCr = nCn-r ⇒ nC7= nCn-7 ⇒ nCn-7= nC5 ⇒n-7=5 ⇒n=7+5=12 Ans : n=12 Given: nC14 = nC16 To find: nC28=? We know that: nCr = nCn-r ⇒ nC14= nCn-14 ⇒...
Answer : (i) Given: 15C8 + 15C9 – 15C6 – 15C7 To prove: 15C8 + 15C9 – 15C6 – 15C7=0 We know that: nCr = nCn-r ⇒15C8 + 15C9 – 15C6 – 15C7=15C8 + 15C9 – 15C9 – 15C8=0 Hence, proved that 15C8 + 15C9 –...
⇒90C88=4005 Ans: ⇒90C88=4005
⇒16C13 =560 Ans: 16C13=560
⇒20C4 =4845 Ans: 20C4 =4845