Шаблонизатор

let allArrays = [['Путин', 'Обама'], ['введи', 'быстрее вводи'], ['войска', 'армию']];

function allPossibleCases(arr) {
    if (arr.length === 0) return [];
    if (arr.length === 1) return arr[0];

    let result = [];
    let allCasesOfRest = allPossibleCases(arr.slice(1));  // recur with the rest of array
    for (let c in allCasesOfRest) {
        for (let i = 0; i < arr[0].length; i++) {
            result.push(arr[0][i] + ' ' + allCasesOfRest[c]);
        }
    }
    return result;
}

var r=allPossibleCases(allArrays);
console.log(r)