There are 20 identical sticks lined up in a row occupying 20 distinct places as follows: · six of them are to be chosen. (a) how many choices are there? (b) how many choices are there if no two of the chosen sticks can be consecutive? (c) how many choices are there if there must be at least two sticks between each pair of chosen sticks?

a)38760

b)5005

c)210

Step-by-step explanation:

Given that

20 identical sticks

We have to 6 of them

a)

The number of choice will be .

b)

The number of choices  if no two of the chosen sticks can be consecutive will be  .

c)

|xx|xx|xx|xx|xx|

Total seven positions are available

So

4-0-0-0-0-0-0                                                      7!/6!=7

3-1-0-0-0-0-0                                                         7!/5!=42

2-2-0-0-0-0-0                                                        7!/2!5!=21

2-1-1-0-0-0-0                                                        7!/2!4!=105

1-1-1-1-0-0-0                                                           7!/4!3!=35

Now by adding all 7+42+21+105+35=210

13

step-by-step explanation:

169-1=168

168-3=165

165-5=160

160-7=153

153-9=144

144-11=133

133-13=120

120-15=105

105-17=88

88-19=69

69-21=48

48-23=25

25-25=0

since it took 13times to completely subtract it hence its square root is 13

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.