Prístup 1

for (n in 49:55) print(choose(n, 6) - 380 * 10^6)

## [1] -366016184
## [1] -364109300
## [1] -361990540
## [1] -359641480
## [1] -357042520
## [1] -354172835
## [1] -351010325

n.vektor <- 50:100
y <- function(n) choose(n, 6) - 380 * 10^6
plot(n.vektor, y(n.vektor))
abline(h = 0)

choose(83, 6)/10^6  # chceme cca 380

## [1] 377.4471

Prístup 2

EX <- function(n) sum((6:n) * choose((6:n) - 1, 5))/choose(n, 6)

n.vektor <- 49:60
EX.vektor <- n.vektor
for (i in 1:length(n.vektor)) EX.vektor[i] <- EX(n.vektor[i])
plot(n.vektor, EX.vektor)
abline(h = 49)

EX(56)

## [1] 48.85714

11 * choose(56,6) / 10^6  # chceme cca 380

## [1] 357.1528

EX <- function(n) sum((6:n) * choose((6:n) - 1, 5))/choose(n, 6)

n.vektor <- 50:60
EX.vektor <- n.vektor
for (i in 1:length(n.vektor)) EX.vektor[i] <- EX(n.vektor[i])
plot(n.vektor, EX.vektor)
abline(h = 49)

n.vektor <- 30:40
EX.vektor <- n.vektor
for (i in 1:length(n.vektor)) EX.vektor[i] <- EX(n.vektor[i])
plot(n.vektor, EX.vektor)
abline(h = 29)

n.vektor <- 35:45
EX.vektor <- n.vektor
for (i in 1:length(n.vektor)) EX.vektor[i] <- EX(n.vektor[i])
plot(n.vektor, EX.vektor)
abline(h = 35)

Prístup 3

EY <- function(n){
  menovatel <- choose(n,6)^3
  k <- 6:n
  suma1 <- rep(0, length = length(k))
  suma2 <- rep(0, length = length(k))
  for(j in 1:length(k)){
    suma1[j] <- sum(choose(5:(k[j]-1), 5))^3
    suma2[j] <- sum(choose(5:(k[j]-2), 5))^3
  }
  pk <- suma1 - suma2
  return(sum(k * pk)/menovatel)
}

n.vektor <- 49:55
EY.vektor <- n.vektor
for (i in 1:length(n.vektor)) EY.vektor[i] <- EY(n.vektor[i])
plot(n.vektor, EY.vektor)
abline(h = 49)

EY(51)

## [1] 48.91982

21 * choose(51,6) / 10^6

## [1] 378.1987