In a proceeding pursuant to CPLR article 75 to confirm an arbitration award, in which respondent cross-moved to vacate the said award, petitioner appeals from an order of the Supreme Court, Westchester County, dated June 22, 1977, which denied its application and granted the cross motion. Order reversed, on the law, with $50 costs and disbursements, application to confirm granted, and cross motion to vacate denied. The collective bargaining agreement between the parties for the period in issue provides for a bargaining unit composed of "all professional personnel on tenure, on probation, and on terminal appointments” and, under its terms, it is stipulated that no person in the bargaining unit shall be terminated due to budgetary reasons or abolition of programs (cf. Matter of Board of Educ. v Yonkers Federation of Teachers, 40 NY2d 268; Matter of Yonkers Federation of Teachers v Board of Educ., 58 AD2d 607). The grievance involved in this proceeding concerns 29 regular, full-time teachers hired to commence service in September, 1975; they in fact commenced service at that time. According to the Professional Staff Handbook of the Yonkers Board of Education, a superintendent’s letter of appointment and a teacher’s written acceptance thereof and oath, together, constitute a binding contract. In October, 1975 a new plan for budget cuts contemplated the making of no new appointments. The respondent deferred action at first on this plan and the teachers were advised to continue in their positions. On October 16, 1975 the respondent informed the teachers that their appointments were ineffective and that they were now to be considered only substitutes at a lower salary scale. The petitioner then filed the present grievance and sought arbitration. The respondent moved to stay arbitration; that motion was granted by Special Term and affirmed by this court (Matter of Board of Educ. v Yonkers Federation of Teachers, 51 AD2d 568), but was reversed by the Court of Appeals (40 NY2d 268, supra). Upon the arbitration, the only *584issue, by stipulation of the parties, was whether the 29 teachers fell within ' the terms of the collective bargaining agreement. The arbitrator held in favor of the teachers, finding that they were employees of the respondent and were justified by the actions of the superintendent in considering that they had been properly appointed as full-time members of the teaching staff. Special Term, in vacating the award, held that the appointments had not been formally approved by the respondent and that the teachers were not, therefore, part of the bargaining unit under the collective bargaining agreement. As we read the cases dealing with arbitration in the public sector under collective bargaining agreements, it must first be decided whether the grievance lies within an area in which the public employer is free to bargain, and then a decision must be made as to whether the agreement refers the grievance to arbitration (Matter of Acting Supt. of Schools of Liverpool Cent. School Dist. v United Liverpool Faculty Assn., 42 NY2d 509). Here, the past litigation between the parties establishes that the agreement validly covers an area in which the respondent was free to bargain and that the agreement includes within its terms the right to arbitration of the present grievance. Under the limited sphere of interference by the courts in arbitrators’ awards, unless we may say that the arbitrator here was wholly irrational, the award may not be set aside (see Rochester City School Dist. v Rochester Teachers Assn., 41 NY2d 578, 582). We cannot say that the arbitrator was irrational in treating the teachers as employees of the respondent under the circumstances here. The conduct of the respondent, in allowing the teachers to receive appointments from the superintendent by their acceptance of the appointment and signing of an oath and by directing the teachers to begin and continue work, was sufficient to enable the arbitrator to find that it would be inequitable to hold the teachers to a contract, but still subject them to termination at the exclusive will of the respondent. " 'Arbitrators may do justice’ ” (Rochester City School Dist. v Rochester Teachers Assn., 41 NY2d 578, 582, supra), and the award here marks a permissible balance of equity between the parties. Hopkins, J. P., Hargett, Damiani and O’Connor, JJ., concur.